Understanding the kinematics and stress buildup near fault asperities is of paramount importance in assessing seismic hazards. However, the spatiotemporal evolution of slip deficit and shear stress accumulation rates near fault asperities, governed by the rheological behavior of the Earth, remains unclear. To address this gap, a 3D viscoelastic finite element model was developed, incorporating a vertical strike-slip fault with an asperity considered through a contact algorithm to explore spatiotemporal variations in interseismic coupling (ISC) and shear stress accumulation rates. The main conclusions drawn are as follows: (1) Due to the continuity of the medium, although the region adjacent to an asperity is not fully locked, its slip velocity is still lower than the block's movement velocity, resulting in a spatial pattern of decreasing ISC outward from the fault asperity. (2) Viscoelastic effects regulate the deformation near a fault asperity, leading to an increase in the spatial extent of the ISC with time. (3) The ISC can serve as an approximate indicator of the shear stress accumulation rate. Neglecting viscoelastic effects, a value of approximately 0.5 can be used as the threshold for strong locking, and shear stress accumulation is insignificant below this value. This study establishes a meaningful connection between ISC and shear stress accumulation rate, offering valuable insights for identifying potential seismic hazards.