---

Exhibit 31.1

CERTIFICATION PURSUANT TOSECTION 302 OF THE SARBANES-OXLEY ACT OF 2002

I, Kenneth Hicks, certify that:

1.     I have reviewed this quarterly
report on Form 10-Q of Argentex Mining Corporation;

2.     Based on my knowledge, this
report does not contain any untrue statement of a material fact or omit to state
a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with respect
to the period covered by this report;

3.     Based on my knowledge, the financial
statements, and other financial information included in this report, fairly
present in all material respects the financial condition, results of operations
and cash flows of the company as of, and for, the periods presented in this
report;

4.     The registrants other certifying
officer(s) and I are responsible for establishing and maintaining disclosure
controls and procedures (as defined in Exchange Act Rules 13a-15(e) and
15d-15(e)) and internal control over financial reporting (as defined in Exchange
Act Rules 13a-15(f) and 15d-15(f)) for the registrant and have:

(a)       Designed such
disclosure controls and procedures, or caused such disclosure controls and
procedures to be designed under our supervision, to ensure that material
information relating to the registrant, including its consolidated subsidiaries,
is made known to us by others within those entities, particularly during the
period in which this report is being prepared;

(b)      
Designed such internal control over financial reporting, or caused such internal
control over financial reporting to be designed under our supervision, to
provide reasonable assurance regarding the reliability of financial reporting
and the preparation of financial statements for external purposes in accordance
with generally accepted accounting principles;

(c)      
Evaluated the effectiveness of the registrants disclosure controls and
procedures and presented in this report our conclusions about the effectiveness
of the disclosure controls and procedures, as of the end of the period covered
by this report based on such evaluation; and

(d)      
Disclosed in this report any change in the registrants internal control over
financial reporting that occurred during the registrants most recent fiscal
quarter (the registrants fourth fiscal quarter in the case of an annual report)
that has materially affected, or is reasonably likely to materially affect, the
registrants internal control over financial reporting;

5.     The registrants other certifying
officer (s) and I have disclosed, based on my most recent evaluation of internal
control over financial reporting, to the registrants auditors and the audit
committee of the registrants board of directors (or persons performing the
equivalent functions):

(a)      
All significant deficiencies and material weaknesses in the design or operation
of internal control over financial reporting which are reasonably likely to
adversely affect the registrants ability to record, process, summarize and
report financial information; and

(b)      
Any fraud, whether or not material, that involves management or other employees
who have a significant role in the registrants internal control over financial
reporting.

Date: December 14, 2010

/s/ Kenneth
HicksKenneth Hicks President and Director (Principal Executive
Officer)

---