From the summary: We present a general numerical procedure for the computation of corner singularities which appear in the case of non-smooth domains in three-dimensional linear elasticity. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of the problem is approximated by Galerkin-Petrov finite element method. A quadratic eigenvalue problem \(({\mathbf P}+ \lambda {\mathbf Q}+ \lambda^2 {\mathbf R}){\mathbf u}= \mathbf{0}\) is obtained, with explicitly analytically defined matrices P,Q,R. Moreover, the three matrices are found to have optimal structure, so that P,R are symmetric and Q is skew symmetric, which can serve as an advantage in the following solution process. On this foundation a powerfal iterative solution technique based on Arnoldi method is submitted.