Gametophytic self-incompatibility is a widespread genetic system, which enables hermaphroditic plants to avoid self-fertilization and mating with close relatives. Inbreeding depression is thought to be the major force maintaining self-incompatibility; however, inbreeding depression is a dynamical variable that depends in particular on the mating system. In this paper we use multilocus, individual based simulations to examine the co-evolution of self-incompatibility and inbreeding depression within finite populations. We focus on the conditions for the maintenance of self-incompatibility when self-compatible mutants are introduced in the population by recurrent mutation, and compare simulation results with predictions from an analytical model treating inbreeding depression as a fixed parameter (thereby neglecting effects of purging within the self-compatible sub-population). In agreement with previous models, we observe that the maintenance of self-incompatibility is associated with high inbreeding depression and is facilitated by high rates of self-pollination. Purging of deleterious mutations by self-compatible mutants has little effect on the spread of those mutants as long as most deleterious alleles have weak fitness effects: in this case, the genetic architecture of inbreeding depression has little effect on the maintenance of self-incompatibility. By contrast, purging may greatly enhance the spread of self-compatible mutants when deleterious alleles have strong fitness effects.