We perform dynamic simulations of thrust and normal faults over multiple earthquake cycles. Our goal is to explore effects of asymmetric fault geometry on the long-term seismicity and dynamics of dipping faults. A dynamic finite-element method is used to model the interseismic and coseismic processes, with a dynamic relaxation technique for the former. The faults are loaded by stable sliding along the downward continuation of the faults. The asymmetric fault geometry of dipping faults with respect to the free surface cause changes in normal stress during the interseismic and coseismic periods. These changes are of opposite sign in the two periods, resulting in a stabilization of the normal and shear stresses over many earthquake cycles. Both faults develop relatively stable event patterns, in which a large event that ruptures the entire fault is preceded by a number of small events with various rupture lengths. A strong asymmetry in fault and ground motion exists between thrust and normal faults, and between the hanging wall and the footwall of both faults on faults dipping less than 70°. In both normal and thrust faults, the horizontal component of ground motion dominates on the footwall, while the vertical component dominates on the hanging wall. The above results may have implications in seismic hazard analysis and building design in regions where dip-slip faults predominate.