This study provides methods for calculating the mean and variance of the number of animals with the desired genotype in each backcross generation for a marker-assisted introgression experiment. The ultimate goal is to produce animals which are homozygous for the desired loci. The methods have been developed specifically for experiments with inbred lines. The model assumes a Poisson distribution for litter size, and is similar to that used in stochastic versions of population dynamics models. Certain biological parameters must be specified as well as parameters under the control of the breeder. These methods can be utilized in designing an experiment to determine the number of founder animals required, given the number of animals required at the completion of the backcross process and vice versa. Consideration is given to minimizing the total amount of genotyping over the entire experiment, by varying the number of times each backcrossed male is used. In addition, an outline is given for an adaptive design that allows for changes in male usage to be made during the experiment.