Mathematical models with a singularity play a decisive role in predicting the development of processes in fracture mechanics and physics. In the engineering literature, computational methods are widely studied for problems of electromagnetism, hydrodynamics and the theory of elasticity with a singularity caused by the presence of re-entrant corners on the boundary of a domain. We have constructed a weighted finite element method based on the introduction of the definition of an \(R_{\nu }\) -generalized solution for the listed problems . This method allows finding a solution with high accuracy compared to the classical finite element method. At the same time, it retains the simplicity of the stiffness matrix structure, unlike other numerical methods of increased accuracy. To use weighted finite element method effectively, it is necessary to correctly set the control parameters of the approach. In this paper, the weighted finite element method and found the body of optimal parameters for finding an approximate solution to the Lamé system in domains with a boundary containing re-entrant corners in the range from \(\pi \) to \(2\pi \) are presented.