The results of the simulation of the axial shift and twist hollow cylinders of compressed or weakly reinforced filaments weakly compressible elastomeric material in a cylindrically symmetric deformation. Thus these types of deformation of the cylinder may be combined with stretching and inflation. Applicable model reinforced material. Yarns with low density arrangement are replaced by their center lines, endowed with the appropriate mechanical properties. The macroscopic stress is defined as an additive in the matrix due to stress and efforts constrained uniaxial tension or compression reinforcement filaments. On the basis of equations and solutions of the corresponding boundary value problems is studied the deformation of the axial shear and torsion elastic cylinders in the absence and in the presence of the radial threads reinforcement system.