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Exhibit 31.2

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

I, Jeffrey Finkelstein, 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: June 10, 2011

/s/ Jeffrey
FinkelsteinJeffrey
Finkelstein Chief Financial Officer (Principal Financial Officer
and
  Principal Accounting Officer)

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