Safety factors for kinematically admissible failure mechanisms in jointed rock masses have been defined with linear and nonlinear failure criteria for rock discontinuities. Data required to compute these safety factors are obtained by means of two finite element anlayses of the effects of selfweight and external (structural) loading, respectively. Both types of analysis are closely linked since they share a common geometry. Joint elements are used to simulate the behaviour of rock discontinuities. If kinematically admissible mechanisms are possible under field conditions, the finite element mesh should also allow them to develop. Different aspects of the methodology have been illustrated through the safety evaluation of a 150 m high arch dam and its foundation in fractured cretaceous limestone. Special attention has been paid to the modelling of a realistic geometry including three-dimensional rock blocks and discontinuities. The paper discusses the effect of initial state of stress, the evolution of safety as the external load increases and the relation between the defined safety factors. It also provides practical guidelines for conducting this type of analysis in complex situations.