This paper discusses the issue of improving the functional properties of road asphalt pavements by modifying bituminous binder with SBS copolymer. The main purpose of the paper is to assess the resistance to permanent deformations and the temperature susceptibility of polymer-modified road asphalt binders, which are most commonly used in the upper layers of road and airport pavements. The bitumens subject to the study originate from various crude oil deposits (Russian and Venezuelan). They were modified in laboratory conditions with a concentrated additive with the known content of the SBS copolymer of 9%. The result was a asphalt binder containing the known percentage of the SBS copolymer of 1.5%, 3.0%, 4.5% and 6%. The rheological properties of the tested bitumens were determined by use of a dynamic shear rheometer (DSR), and with the application of the sinusoidal variable load, in the broad test temperature spectrum (from 40°C to 100°C). The analysis of the values of the dynamic shear modulus |G*| of all the studied bitumens shows that the increase in the content of SBS copolymer in the tested binder increases the value of |G*|, which may result in higher resistance to permanent deformations of road pavements caused by repeated traffic loads, especially in the case of pavements operated at high temperatures. The asphalt mixtures resistance to rutting is one of the basic parameters related to road pavement service-life, affecting both the safety and driving comfort of users.