Self-pierce riveting (SPR) is a sheet material joining technique which is suitable for joining dissimilar materials, as well as coated and pre-painted materials. Published work relating to finite element analysis of SPR joints is reviewed in this paper, in terms of process, static strength, fatigue strength, vibration characteristics and assembly dimensional prediction of the SPR joints. A few important numerical issues are discussed, including material modelling, meshing procedure, failure criteria and friction between substrates and between rivet and substrate. It is concluded that the finite element analysis of SPR joints will help future applications of SPR by allowing system parameters to be selected to give as large a process window as possible for successful joint manufacture. This will allow many tests to be simulated that would currently take too long to perform or be prohibitively expensive in practice, such as modifications to rivet geometry, die geometry or material properties. The main goal of the paper is to review recent progress in finite element analysis of SPR joints and to provide a basis for further research.