Abstract
We consider a boundary value problem for a system of the fourth order pseudo-hyperbolic equations with nonlocal condition on a rectangular domain. By introducing a new unknown function, the considered problem is reduced to an equivalent nonlocal problem with integral condition for a system of hyperbolic integro-differential equations of the second order. We propose an algorithm for finding an approximate solution to the equivalent problem, and its convergence is proved basing on the functional parametrization method. Sufficient conditions of the unique existence of the classical solution to the boundary value problem for the system of the fourth order pseudo-hyperbolic equations with nonlocal condition are established in the terms of initial data.