Modern lasers are unable yet to cause electron-positron pair production in vacuum, however it is possible to notice considerable influence of vacuum polarization on radiation that propagates in such medium. In our work we present nonlocal theory of interaction of intensive laser radiation with electron-positron vacuum. We refuse from Heisenberg-Euler approximation and it permits us to calculate nonzero response of vacuum even for a plane wave. We show how to use the "proper time" method for calculation of corrections to the Maxwell equations. These equations are solved for the case of plane wave and their solutions are investigated.