The effective numerical algorithm to solve a wide range of plane elasticity problems is presented. The method is based on the use of the complex hypersingular boundary integral equation (CHBIE) for blocky1 systems and bodies with cracks and holes. The BEM technique is employed to solve this equation. The unknown functions (displacement discontinuities (DD) or tractions) are approximated by Lagrange polynomials of the arbitrary degree. For the tip elements the asymptotics for the DD are taken into account. The boundaries of the blocks, cracks and holes are approximated by the arcs of the circles and the straight elements. In this case all the integrals (hypersingular, singular and regular) involved in this equation are evaluated in a closed form. Numerical results are given and compared either to the ones obtained by the other authors or to analytical solutions.