Abstract Computational methods for three finite element analysis programs have here been implemented and developed in this work. 1. FEM program shows an analysis of straight or curved thin-walled girders. 2. Analysis of solid beam-structures - 3D Timoshenko beam element. Comparisons of the results are made. 3. Analysis of plate and shell structures in a geometrically non-linear way. To perform the algebraic caluculation for the element, expressions mathematical software has been used. This makes it possible to obtain analytical and computationally efficient expressions for the stiffness matrices and force vectors.