Аннотация:The paper investigates nonlinear effects found in the exact analytical solution of problem of multiple superimposition of large tensile-compressive and torsion strains for a sequentially formed multilayer cylinder, each layer of which is made of a hypoelastic incompressible material. After attaching each layer, tension-compression and torsion of the composite cylinder are performed. The material of each layer constituting the cylinder is characterized by a constitutive relationship, including the objective corotational derivative of Jaumann or Dienes. Based on the description of the formation and deformation of the cylinder, a mathematical statement of the problem is given and the main steps of its analytical solution are described. Some numerical results are given. The presence of the Poynting effect is demonstrated.