The influence of thermoplastic elastomers, which are two-block statistical block copolymers based on polybutylene terephthalate and polytetramethylene oxide with a different ratio of rigid and elastic blocks, on the static and dynamic mechanical properties of epoxy polymers is studied. The initial compounds for the synthesis of block copolymers are dimethyl terephthalate, 1,4-butanediol and polytetramethylenoxide with a molecular weight of 2000. The tetrabutoxide is used as catalyst. The process of interaction of the initial components is carried out in two stages, the reaction of transesterification and copolycondensation is consistently carried out. The composition of BSP is set by the ratio of initial reagents. The total molecular weight of block copolymers is 30–40 thousand. The method of dynamic mechanical analysis shows that the introduction of modifiers leads to a decrease in molecular mobility in a wide temperature range from low-temperature (at 220K) to high-temperature (at 380K) relaxation transitions. The magnitude of the effect depends on the ratio of rigid and flexible blocks in the block copolymer. It is assumed that the decrease in the tangent of the angle of mechanical losses at temperatures below the glass transition temperature and especially in the region of the β-transition, may be associated with the slowdown of relaxation processes at the interface of the epoxide matrix with rigid blocks of thermoplastic elastomer. The observed effects in the region of high-temperature transition may be associated with the restriction of freedom of conformational rearrangements near the interface of the epoxy polymer with polybutylene terephthalate and polytetramethylene oxide blocks and an increase in the cross-linking density of the epoxy. A noticeable decrease in the magnitude and creep rate of epoxy composites is found when thermoelastoplast is introduced.