A valuable probe for examining relativistic gravity, star stricture, and the dynamical development of near binary systems is the apsidal motion of a non-synchronous binary pulsar. In this study, we examine the combined effects of tidal interaction, star oblateness, and general relativity on the apsidal motion of three binary pulsars: J0621+1002, J0737-3039A/B, and 1913+16. Tidal effects and their role in orbital and spin evolution were described by numerical integrations using Zahn’s tidal equations (Astron. Astrophys. 57:383–394, 1977, Astron. Astrophys. 220:112–116, 1989). We calculated the orbital circularization and tidal synchronization timescales for each system. The simulated results show a clear trends of decreasing of both the semi-axis and eccentricity, while increasing the spin rate. In addition, the tidal effects play only a minor role in orbital decay compared with energy loss due to gravitational wave emission. Both the obtained apsidal motion constants [ $k\simeq 0.1$ ] and the derived tidal friction periods, which vary from a few hours to several days, correspond well with theoretical estimates. This is demonstrated in the compact system PSR1913+16, where gravity radiation causes the orbital period to decrease by approximately 76.5 μs/yr. While the wider system J0621+1002 displays minor orbital change over timescale exceeding 1010 yrs, the double pulsar J0737-3039A/B exhibits faster orbital evolution, with synchronization occurring in about 8.4 $\times 10{^{3}}$ yrs. The results demonstrate the significance of relativistic effects in neutron star binaries and the necessity of incorporating gravitational wave terms in long-term orbital evolution.
