The reinforcement model of speciation holds an important place in modern evolutionary thought. A closer examination of the model using a computer simulation reveals that there are a number of implicit assumptions necessary for reinforcement to work. 1. It requires that reproductive characters form part of an open genetic system with high heritability and that there is considerable variability within this system. 2. The two strains must coexist throughout the period in which selection is acting. This requires intense frequency-dependent selection to counteract the inherently unstable selection regime of negative heterosis. The necessary intensity suggests that extinction of one of the strains is the more likely outcome unless there are substantial initial differences in reproductive characters. Furthermore, chance extinction of one of the strains cannot occur in this selection period. 3. The net cost of assortative characters must be less than the cost of a greater probability of producing hybrid offspring. This is a complex matter with several opposing factors. 4. The fitness of the hybrids must be zero or close to it and must remain so. 5. The selective pressure for assortative reproductive characters becomes weaker as these characters are established. It appears unlikely that selection alone could complete the process, as is hypothesized in some formulations of the model. Further data from natural populations and laboratory experiments are required to clarify several of these points, especially the first. These problems do not mean that reinforcement can never occur, but they do imply that speciation by reinforcement is not nearly as prevalent as much of the biological literature suggests.