There are a number of procedures for estimating variance components in the case of unbalanced data by equating certain mean squares to their respective expectations. Variances of the resulting estimates are derived for one such procedure applied to a three-way classification. The variances are obtained by a procedure based on the work of Searle [1956]. The model considered herein includes a fixed main effect, two random main effects and a random interaction effect. It is assumed that all random effects are normally distributed. Unbiased estimates of the variances are derived. The two-way random model with interaction and the two-way mixed model without interaction are included as special cases.