A split plot design for the factorial treatment combinations of factors A and B with t and s levels respectively, consists of wholeplots made up of s subplots or experimental units with each level of A applied to r wholeplots and the levels of B applied to the s subplots within each wholeplot. Often this process increases the amount of information for the estimates of the main effect B and the interaction A X B at the expense of information for the main effect A. There may arise situations where the number of subplots in each wholeplot is restricted to say, kc < s. An incomplete split plot design can now be set up with each level of factor A applied to r wholeplots and the s levels of factor B arranged in a balanced incomplete block design within each level of factor A by considering the wholeplots as blocks. That is, on a particular level of factor A each level of factor B occurs R times and each pair of levels of factor B occur in the same wholeplot X times, where R = rk/s and X = R(k l)/(s 1). Here r must be chosen so that the design exists and in some cases this may be so large that it will be impractical. Throughout this paper the wholeplot design will be considered as a conmpletely randomized design. However, it will sometimes be possible to have block designs for the wholeplots, but these will not be considered here.