An algorithm of solution of the problem of bending torsion of the rod based on R-function method is considered in the paper. The algorithm of integration of the systems of resolving equations on the basis of Rvachеv’s R-function method (RFM) and the method of progressive approximation is developed. Computing algorithm of elastic bodies of arbitrary section and software of stress-strain state study of elastic prismatic bodies of arbitrary section with a cavity is given. The examples of validity of design algorithm of elastic prismatic bodies and software functioning are also given in the paper.