We study the applicability of the methods of perturbation theory for solution of problems of lateral bending of plates with uniformly stressed reinforcement of constant cross section. Based on these methods, the two-dimensional solutions for corresponding boundary-value problems are obtained. We reveal the nonuniqueness of solutions of such problems and propose the procedure of control on a set of projects with uniformly stressed reinforcement. Results of comparison of exact and approximate solutions for simply connected and doubly connected plates are presented.