The Gauss hypergeometric distribution with the density proportional to x 1 (1 x) 1 (1 +x ) , 0 < x < 1 arises in connection with the prior distribution of the parameter (0 < < 1) representing trac intensity in aM=M=1 queue system. In this article, we define and study a multivariate generalization of this distribution and derive some of its properties like marginal densities, joint moments, and factorizations. A data application is given. 2000 AMS Classification: Primary 33E99; Secondary 62H99.