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Two numerical techniques for solving optimal periodic control problems with a free period are developed. The first method uses shooting techniques for solving an appropriate boundary value problem associated with the necessary conditions of the minimum principle. A convenient form of the transversality condition for the free period is incorporated. The second method is a direct optimization method that applies non‐linear programming techniques to a discretized version of the control problem. Both numerical methods are illustrated in detail by a non‐convex economic production planning problem. In this model, the π‐test reveals that the steady‐state operation is not optimal. The optimal periodic control is computed such that a complete set of necessary conditions is verified. The solution techniques are extended to obtain the optimal periodic control under various state constraints. A sensitivity analysis of the …