In this paper, using the modified applied theory of variable thickness plates, a mathematical model for solving the problem of bending a beam of variable thickness is constructed. A beam of variable thickness with a certain length, subjected to a uniformly distributed load, is considered. In addition to the boundary conditions observed at the edges, it is assumed that there is an additional condition in the middle part of the beam. The study of the problem is reduced to solving a system of differential equations with variable coefficients, corresponding to the boundary conditions. Based on the numerical results obtained using the collocation method, a numerical analysis is performed. Based on the change in the coordinate of the point where the additional condition is applied, optimization was performed, and the optimal solution was determined using a specific criterion.