Based on the conception of ″Production Speed,″ a multistage production system was defined as a technological sequence of production stages where the production time and cost are specified as a function of production speed, and the basic mathematical models of the multistage production system were established. Under three kinds of evaluation criteria - the minimum time, the minimum cost, and the maximum profit rate, the optimal production speeds to be utilized at each production stage and the optimal cycle time were theoretically analyzed, and the computational algorithms for determining them were developed. Practical applicability of the algorithms were proven by solving the optimization problem of the multistage manufacturing system.