[Abstract of thesis.]
The thesis deals with the iterative solution of systems of linear algebraic equations arising from the discretization of the boundary value problem of elasticity. The first part of this work is devoted to preconditions conjugate gradient method with preconditioning given by approximate factorization of the separate displacement component part of the stiffness matrix. Multilevel method with correction by aggregation of unknowns are considered in the second part of this work. We study the convergence rate and suggest use of overcorrection to accelerate the convergence of the method.