Inferences concerning the variance ratios of a random linear model are important in genetics and other areas of scientific investigation. For example, in genetics, the heritability parameters are functions of the variance ratios of a random model. This paper derives simultaneous confidence intervals for all or certain subsets of the parameters of a balanced incomplete random model. This procedure is based on the mean squares of the analysis of variance, and the mean squares are linear functions of a set of minimal sufficient statistics for estimating the parameters of the model. The procedure is demonstrated for a layout of six treatments, ten blocks, and five observations per block.