Motivated by experimental designs for drug combination studies,in this paper,we propose a novel approach for generating a uniform distribution on an arbitrary tetragon in two- dimensional Euclidean space IR2.The key idea is to construct a one-to-one transformation between an arbitrary tetragon and the unit square [0,1]2.This transformation then provides a stochastic rep- resentation for the random vector uniformly distributed on the tetragon.An algorithm is proposed for generating a uniform distribution in an arbitrary triangular prism in IR3.In addition,we devel- op methods for generating uniform distributions in a class of convex polyhedrons in n-dimensional Euclidean space IRn.In particular,stochastic representations for uniform distributions in regions with order restrictions are presented.We apply the proposed method to the experimental design for a drug combination study.