Problems of physical (atomic and molecular) nature of the plastic deformation of polymers and composite materials based on them, despite numerous studies, has not yet been fully resolved. The paper presents the results of the tensile test of composite specimens based on ED-20 epoxy resin with filling of CT-3K carbon textile including the cyclic variation of the mechanical stress up to the fracture of the specimen. For more information about the status of the specimens X-ray diffraction, scanning electron microscopy, and differential scanning calorimetry have been used. We determined the tensile strength, effective modulus of elasticity, hysteresis loss. The resin in the composite had an amorphous structure. The magnitude of the thermal effect upon curing of the composite is proportional to resin fraction. It is shown that the fracture of the composite is predominantly brittle, although plastic component is always present. The strength characteristics of the composite are naturally higher than that of pure cured resin. However, the complex non-linear nature of the dependence of the effective composite module from mechanical stress qualitatively identical to similar dependence of cured resin. The magnitude of the hysteresis losses in mechanical cycling of the composite is significantly higher than that of pure resin but loss dependence on the number of cycles qualitatively identical with the similar dependence for pure resin. A small number of tension-compression cycles leads to a stabilization of quantitative parameters of deformation, and the nature of their dependency on the stress and the number of cycles. The results are interpreted in favor of the assumption that there are some similar mechanisms of deformation of polymeric materials and crystalline solids.