A new method is developed to efficiently compute exact Scheffé-type confidence intervals for output (or other function of parameters) g(β) derived from a groundwater flow model. The method is general in that parameter uncertainty can be specified by any statistical distribution having a log probability density function (log pdf) that can be expanded in a Taylor series. However, for this study parameter uncertainty is specified by a statistical multivariate beta distribution that incorporates hydrogeologic information in the form of the investigator's best estimates of parameters and a grouping of random variables representing possible parameter values so that each group is defined by maximum and minimum bounds and an ordering according to increasing value. The new method forms the confidence intervals from maximum and minimum limits of g(β) on a contour of a linear combination of (1) the quadratic form for the parameters used by Cooley and Vecchia (1987) and (2) the log pdf for the multivariate beta distribution. Three example problems are used to compare characteristics of the confidence intervals for hydraulic head obtained using different weights for the linear combination. Different weights generally produced similar confidence intervals, whereas the method of Cooley and Vecchia (1987) often produced much larger confidence intervals.