In this paper, we consider the problem to determine the stress-strain state of the boundary layer near the edge of the strip of orthotropic material under the applied at the end of self-balanced load (the effect of the Saint-Venant). It is shown that the boundary layer in the orthotropic material penetrates much further than in an isotropic material, which leads to the necessity of calculation. However, the practical difficulties of the calculating the stress-stain of orthotropic materials due to the fact that the characteristic equation of this problem includes both real and complex roots, which makes the numerical implementation of the task difficult. In this paper we purpose a numerical realization of this problem, in which we can get good enough results to determine the stress-stain state of the boundary layer with a minimal number of algebraic equations to determine the constants of integration from the sale of the static boundary conditions at the end of the strip method collocations. The numerical results were obtained.