Inclusion Criteria:  For inclusion in the study, patients should fulfill the following criteria:  Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations.  Diagnosis of unresectable HCC confirmed pathologically or made according to  American Association for the Study of Liver Diseases (AASLD) practice guideline 2010:  patients with cirrhosis of any etiology and patients with chronic hepatitis B (HBV) who may not have fully developed cirrhosis, the presence of liver nodule >1cm and demonstrated in a single contrast-enhanced dynamic imaging [either computed tomography (CT) or magnetic resonance imaging (MRI)] of intense arterial uptake and "washout" in portal venous and delayed phases.  Adult male or female aged >18 years at time of study entry Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1 Body weight >30kg Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply: Women <50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy). Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses >1 year ago, had chemotherapy-induced menopause with last menses >1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy). Must have a life expectancy of at least 12 weeks Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up. Tumor size 5-25cm and number of lesions ≤3 Portal vein involvement (Vp1-3) is allowed: Vp1, presence of a tumor thrombus distal to, but not within, the second-order branches of the portal vein; Vp2, presence of a tumor thrombus in the second-order branches of the portal vein; Vp3, presence of a tumor thrombus in the first-order branches of the portal vein. Liver volume minus gross tumor volume (GTV) > 700cc Child-Pugh liver function class A-B7 No prior immunotherapy Subjects with confirmed concomitant HBV infection (defined as HBsAg positive or HBV DNA detectable) that are eligible for inclusion must be treated with antiviral therapy (per local institutional practice) prior to enrollment to ensure adequate viral suppression (HBV DNA < 2000 IU/mL), must remain on antiviral therapy for the study duration, and continue therapy for 6 months after the last dose of investigational product(s) At least one measurable lesion according to RECIST v1.1.  Adequate normal organ and marrow function as defined below:  Haemoglobin ≥ 9.0 g/dL Absolute neutrophil count (ANC ≥1.5 (or 1.0) x (> 1500 per mm^3) Platelet count ≥ 75 x 109/L (>75,000 per mm^3) Serum bilirubin ≤1.5 x institutional upper limit of normal (ULN). AST (SGOT)/ALT (SGPT) ≤2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be ≤5x ULN Measured creatinine clearance (CL) >45 mL/min or Calculated creatinine clearance CL>45 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance:  Exclusion Criteria:  Patients should not enter the study if any of the following exclusion criteria are fulfilled:  Participation in another clinical study with an investigational product within 4 weeks prior to the first dose of study treatment Concurrent enrolment in another clinical study, unless it is an observational (noninterventional) clinical study or during the follow-up period of an interventional study  Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria  Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after consultation with the Study Physician. Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with Durvalumab or Tremelimumab may be included only after consultation with the Study Physician.  Any concurrent chemotherapy, IP, biologic, or hormonal therapy for cancer treatment.  Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable.  Prior radiotherapy to the region of liver or selective internal radiotherapy Major surgical procedure (as defined by the Investigator) within 28 days prior to the first dose of IP. Note: Local surgery of isolated lesions for palliative intent is acceptable. History of primary immunodeficiency or allogenic organ transplantation.  Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease [e.g., colitis or Crohn's disease], diverticulitis [with the exception of diverticulosis], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome [granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc]). The following are exceptions to this criterion:  Patients with vitiligo or alopecia Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement Any chronic skin condition that does not require systemic therapy Patients without active disease in the last 5 years may be included but only after consultation with the study physician Patients with celiac disease controlled by diet alone Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent  History of another primary malignancy except for  Malignancy treated with curative intent and with no known active disease ≥5 years before the first dose of IP and of low potential risk for recurrence Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease Adequately treated carcinoma in situ without evidence of disease History of leptomeningeal carcinomatosis Presence of extra-hepatic metastases (M1). Patients with suspected brain metastases at screening should have an MRI (preferred) or CT each preferably with IV contrast of the brain prior to study entry. Has untreated central nervous system (CNS) metastases and/or carcinomatous meningitis identified either on the baseline brain imaging (RECIST)) for details on the imaging modality) obtained during the screening period or identified prior to signing the ICF. History of active primary immunodeficiency Active infection including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and TB testing in line with local practice), hepatitis B (known positive HBV surface antigen (HBsAg) result), hepatitis C, or human immunodeficiency virus (positive HIV 1/2 antibodies). Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA.  Current or prior use of immunosuppressive medication within 14 days before the first dose of Durvalumab or Tremelimumab. The following are exceptions to this criterion:  Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or its equivalent Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication)  Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note:  Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to 30 days after the last dose of IP.  Female patients who are pregnant or breastfeeding or male or female patients of reproductive potential who are not willing to employ effective birth control from screening to 90 days after the last dose of Durvalumab monotherapy or180 days after the last dose of Durvalumab + Tremelimumab combination therapy. Known allergy or hypersensitivity to any of the study drugs or any of the study drug excipients. Prior randomisation or treatment in a previous Durvalumab and/or Tremelimumab clinical study regardless of treatment arm assignment.  Patients who have received prior anti-PD-1, anti-PD-L1 or anti-CTLA-4:  Must not have experienced a toxicity that led to permanent discontinuation of prior immunotherapy. All AEs while receiving prior immunotherapy must have completely resolved or resolved to baseline prior to screening for this study. Must not have experienced a ≥Grade 3 immune related AE or an immune related neurologic or ocular AE of any grade while receiving prior immunotherapy. NOTE: Patients with endocrine AE of ≤Grade 2 are permitted to enroll if they are stably maintained on appropriate replacement therapy and are asymptomatic. Must not have required the use of additional immunosuppression other than corticosteroids for the management of an AE, not have experienced recurrence of an AE if re-challenged, and not currently require maintenance doses of > 10 mg prednisone or equivalent per day.  Contraindicated of SBRT:  Any one hepatocellular carcinoma > 25 cm Total maximal sum of hepatocellular carcinoma > 30 cm More than 3 discrete hepatic nodule Direct tumor extension into the stomach, duodenum, small bowel, large bowel, common or main branch of biliary tree Main portal vein, contralateral portal vein, (Vp4) or inferior vena cava (IVC) thrombosis / involvement Presence of clinically meaningful ascites as ascites requiring non pharmacologic intervention (eg, paracentesis) or escalation in pharmacologic intervention to maintain symptomatic control Hepatic encephalopathy Active or prior documented gastrointestinal variceal bleeding