In a normal simulation run, the states of the model are sampled in proportion to their natural frequency of occurrence. For a given sampling effort, this does not in general estimate a given statistic of the model with maximum precision. A sampling theory of Markov chains is developed which allows some statistics of the Markov state frequencies to be estimated with minimum variance for a given sampling effort. A technique is presented to allow the sampling frequency of the states of the simulation to be independent of their natural frequency. By representing a simulation model as a Markov chain, the theory is applied to estimate some statistics of the simulation model with minimum variance; for instance, the frequency of overload of a teleprocessing computer system. A numerical case is presented in which the sampling effort is reduced by a factor of sixty compared to a normal simulation run. © 1972, ACM. All rights reserved.