<p>This work is devoted to the development of approximate solutions of boundary value problems in a rectangular domain for one-dimensional and multidimensional hyperbolic integro-differential equations, which serve as mathematical models of moisture and salt movement in soils. Within the framework of the study, difference schemes were constructed for the initial differential problems. Using the method of energy inequalities, a priori estimates were obtained for solutions of these problems in difference form. Based on these estimates, the uniqueness and stability of solutions were established depending on the initial conditions and the right-hand side, and the convergence of the difference solution to the solution of the corresponding differential problem with an accuracy corresponding to the order of the approximation error was shown.</p>