Many procedures for deriving the Moore-Penrose inverse X^+ have been developed, but the explicit forms of Moore-Penerose inverses for design matrices in analysis of variance models are not known heretofore. The purpose of this paper is to find explicit forms of X^+ for the one-way and the two-way analysis of variance models. Consequently, the Moore-Penerose inverse X^+ and the shortest solutions of them can be easily obtained to the level of pocket calculator by way of our results.