The simultaneous interval estimation for a given set of linear combinations of means whose estimates are jointly normally distributed is treated. In order to give the exact confidence intervals,t2M, the maximum of several quasi-independentt2-statistics, is introduced. Using the inclusion-exclusion formula, a procedure and tables are given for obtaining a good approximation to the exact upper percentage point oft2M. As illustrative examples, the procedure is applied to the interval estimations for parameters in the model of a randomized block design and for coefficients in a normal regression equation.