Inclusion Criteria:  Children aged 7-12 years CPTS-RI total score ≥40 Primary diagnosis of PTSD (6 months or more after the traumatic event) Heart rate ≥ 55 bpm Systolic blood pressure ≥ 95 mm Hg Affiliation to a social security scheme Written consent signed by the parents/holders of parental authority and the investigator Acceptance of the protocol by the child-Child and Parents/Holders of parental authority fluent in French  Exclusion Criteria:  Age<7 years or ≥13 years Children whose parents have been deprived of their authority Contraindication to propranolol (cardiogenic shock, sinus bradycardia, hypotension (< fifth percentile oscillometric or <2SD) (Banker et al., 2016 - see APPENDIX 1), greater than first-degree heart block, heart failure, bronchial asthma and hypersensitivity to propranolol hydrochloride) Concurrent medication with possible interactions with propranolol (cf 8.2) Concurrent psychotropic drugs that have been shown to be effective in improving symptoms of PTSD (Antidepressants, atypical antipsychotics, mood stabilizers) Concurrent psychotherapy (>1 structured session/month declared by the clinician who follows the child) Current active psychosis, anorexia nervosa, bulimia nervosa, binge-eating disorder, attention-deficit hyperactivity disorder, autism spectrum disorder Children with psoriasis Children with a predisposition to hypoglycemia Obsessive-compulsive disorders Bipolar Disorders Mental retardation, Traumatic brain injury (loss of consciousness > 10 minutes) Currently treated with a bradycardic drug Concurrent participation to another interventional study Renal or Hepatic Impairment Pregnancy