Abstract: A high-accuracy time-domain formulation for the seismic hydrodynamic pressure on the vertical up-stream face of dam is proposed, which couples with the dam finite element model to consider the dam-reservoir interaction. The numerical model of the semi-infinite reservoir is thus avoided. In frequency domain, the exact relationship between hydrodynamic force and total horizontal motion is obtained based on the analytical solution of reservoir and the dam-reservoir interface condition. This relationship is transformed into the high-accuracy time-domain formulation with auxiliary functions by using the temporal convolution localization method proposed by authors. This formulation, in spatially and temporally discrete form, can be incorporated into the dam model, leading to the dynamic equations of a dam-reservoir system, which is solved by an explicit algorithm developed by authors. It is implemented by an UEL module of ABAQUS so that the commercial code can be used to analyze a seismic nonlinear dam-reservoir interaction problem, and the UEL module can couple with the dam model in construction of the finite element model, avoiding any special treatment such as restart in solution process. Application of this new formulation to hydrodynamic pressure on a rigid dam demonstrates that the solution is stable and agrees very well with the analytical results. A seismic response analysis of Koyna gravity dam is also given.