The rock mechanical behavior and damage characteristic is of great importance for in situ stress evaluation, wellbore stability analysis and hydraulic fracturing design. The velocities of elastic waves are usually reduced in the presence of rock damage, it may be used for determining the progressive damage of the rock. Therefore, this paper aims to investigate the damage characteristics of transversely isotropic tight sand formation, the rock mechanical and damage parameters in the vicinity of the wellbore were calculated using acoustic logging data. The results indicated that the Poisson's ratio and damage parameters decrease with increasing in radial distance, while the elastic modulus and Thomsen’s coefficients increase. At the same radial position, the vertical elastic modulus is smaller than that of the horizontal, the degree of anisotropy for P-wave is greater than that of S-wave, and the horizontal damage parameter is greater than that of the vertical, which indicated that the micro-cracks near the wellbore mainly occur in the horizontal direction. The changes in mechanical parameters, Thomsen’s coefficients and damage parameters rapidly changed in the range of 1.0–1.8 times of borehole radius. The variations of Thomsen’s coefficients and damage parameters in mudstone are obviously greater than that of sandstone, which may be due to the induced damage between rocks and drilling fluid of mudstone is much higher than sandstone.