The textbook presents an integrated approach to solving the problems of elastic-plastic deformation of materials in large deformations, including experimental studies and numerical modeling. To assess the change in the deformation fields of laboratory samples during the loading process, a recording system based on a digital camera combined with a computer is proposed. For computer modeling of the processes of deformation of elastic-plastic rotation bodies (samples), a defining system of equations in a generalized two-dimensional formulation, including torsion, variational-difference method and numerical solution algorithm. is formulated. The results of experimental and numerical studies of the processes of deformation and destruction of axisymmetric samples and structural elements under combined monotonous loads by torsion-stretching to destruction are presented (sequential load by stretching and torsion, (Spreading and stretching)......... ] .................. The textbook is useful in the performance of term papers and diplomas and the acquisition of practical skills in solving applied problems of mechanics and mathematical physics by students of the Faculty of Mechanics and Mathematics (areas "Applied mathematics and computer science", "Mechanics") .