Two probabilistic Shake-and-Bake algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities. The algorithms proceed by generating a random sequence of points on the boundary of a polyhedron, and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence. The limiting distribution of the sequence of points generated by the algorithms is proven to be uniform on the boundary of the polyhedron.