Tax Return Due Date Simplification and Modernization Act of 2013 - Amends the Internal Revenue Code to change tax return due dates for partnerships (from April 15 to March 15, with a six-month extension), S corporations (from March 15 to March 31), and C corporations (from March 15 to April 15).

Requires the Secretary of the Treasury, for taxable years beginning after December 31, 2013, to modify by regulation the due dates for extensions of tax returns for partnerships, trusts and estates, employee benefit plans, tax-exempt organizations, and certain trust funds. Sets a due date of April 15 for the annual information return of a foreign trust with a U.S. owner and for the report of foreign bank and financial accounts (with extensions until October 15).

Extends the automatic extension for corporation income tax returns from three to six months.