||Summary This paper presents an elasto-viscoplastic block element method and its application to the deformation and stability study of arch dam abutment slopes. The paper is composed of two parts. The first part concerns the numerical methods used in the analysis, which includes the identification of the rock blocky system, the algorithm of unconfined seepage flow in discontinuity network taking the grout curtain and drainage curtain into account, and the elasto-viscoplastic block element method as well. In the second part a complicated arch dam abutment slope is studied, from which the seepage flow, the deformation, and the safety factor of the abutment slope are obtained. Based on the analysis suggestions about the seepage control and stabilization measures are made.