ABSTRACT: Experimental insemination was performed using artificially produced low-motility sperm. A mathematical model was applied to the results of the insemination in order to clarify the relationship between sperm motility, the density of sperm and the fertilization rate of eggs. In the model, the probability of fertilization by individual spermatozoa was a function of sperm density in the insemination solution. The results showed that the probability of fertilization clearly decreased with increased sperm density, and the maximum possible fertilizing rate by increasing the sperm density was constrained by the proportion of motile sperm (% motility). The model was also applied to the results of insemination tests of cryopreserved sperm in order to evaluate the fertilizing capacity of cryopreserved sperm. It was proven that cryopreserved sperm needed a higher density to obtain the maximum fertilization rate compared with fresh sperm, and it was anticipated that the ratio of the motile inseminated cryopreserved sperm should be more than 5.0% to achieve an egg fertilization rate greater than 90%.