Mechanical and structural properties of polypropylene (PP) block copolymer irradiated with 5 MeV electron beam irradiation (absorbed doses 25 – 150 kGy) have been investigated. Increase of the strength-strain characteristics of PP modified with bisphenol a dimethacrylate monomer (BAD) as the cross-linking agent with concentration of 0.5 – 3 wt.% have been researched. Properties of materials grafted with BAD have been investigated by the methods of differential scanning calorimetry and infrared spectroscopy. Thermorelaxation (σTR, MPa) and residual stresses (σRS, MPa) caused by isometric heating and subsequent cooling of irradiated and oriented (ε = 100%) samples with 3 wt.% BAD have been measured. Thermorelaxation (σTR, MPa) and residual stresses (σRS, MPa) have indicated a relatively high efficiency of cross-linking. Increase of mechanical properties (E, σb, and εb) at absorbed doses 25 - 150 kGy with increase in the content of BAD in comparison to entire PP has been determined.