Senate Finance Committee chairman Robert J. Dole (R-Kan.) yesterday said he had written President Reagan and the leaders of the House and Senate urging them to call a post-election session of Congress to deal with the problem of Social Security.

Dole said such a session was "imperative" and that he wrote Reagan, Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) and House Speaker Thomas P. O'Neill Jr. (D-Mass.) that without such a lame-duck session Congress is unlikely to legislate on Social Security. By next July, Dole warned, the Social Security trust fund would have reserves equal to only 10 weeks of benefits.

Despite a widespread belief that some measures are needed to reduce the future costs of the Social Security program, the political dangers of calling for Social Security changes have so far stopped any move to cut benefits or save money on the program. Reagan backed off from cuts last year and this year after a political outcry.

Dole had previously announced on television his intention to push for a post-election session, provided there were not too many changes in Congress. In his letters he said there would be a "real window of opportunity" after the November elections to reach a bipartisan consensus on how to save money for the system.

The White House does not yet seem very enthusiastic about the idea of such a lame duck session, and Dole told reporters yesterday that he was receiving "indications from the White House that I shouldn't be pushing so hard" for one. However, he said that the National Commission on Social Security Reform, set up by Reagan to produce reform recommendations, "should be able to report . . . shortly after the election."

The Senate Finance Committee and the House Ways and Means Committee could meet a week before the full Congress to see if a bipartisan agreement on the issue was possible, Dole said.

When the 98th Congress starts "there is no question that [it] will be faced with the need to enact major new deficit-reduction measures," Dole said.