The article shows how to construct simple numerical examples in two‐way ANOVA, specifically randomized blocks, balanced two‐way layouts, and Latin squares, such that the estimated effects and the residual standard deviation(ssay) are preset whole numbers. Working through simple numerical problems is helpful to students meeting a technique for the first time, to be followed by (computer‐based) analysis of larger, real datasets when the basic mechanics of the method are understood. This work extends that of Read (1985) on one‐way ANOVA and effectively completes the coverage of layouts met in elementary experimental design. First, the user defines an estimated mean and set of effects appropriate to his chosen layout and to the context in which the data are set, along with the value ofs.The estimated effects are essentially arbitrary, and so the significance or insignificance of a set of effects, of contrasts between them or of interactions, may be demonstrated on datasets designed for the purpose. The second step, to find a residual vector satisfying the side‐conditions implied by the estimating equations, is managed by simple table look‐up procedures. Adding the residual vector to the structural effects then gives the data for analysis. An example is given of each layout discussed.