Numerical limit analysis is used to determine rigorous lower and upper bounds to the horizontal critical pseudo-static seismic coefficient k_c required to cause collapse of two-dimensional slopes. Optimal bounding values of k_c are calculated by applying linear programming techniques. Additionally, conventional displacement finite element analyses were performed for selected cases using the program ABAQUS. The values of k_c and the slip surfaces obtained from the displacement finite element analyses and numerical limit analysis are in good agreement with those from both limit equilibrium methods and log-spiral upper bound method. A small number of finite element analyses using a non-associated flow rule showed that soil dilatancy influences the value of k_c, and that limit analysis and limit equilibrium solutions may be slightly unconservative.