  The regularity theory for variational inequalities over polyhedral sets
developed in a series of papers by Robinson, Ralph and Dontchev-Rockafellar in
the 90s has long become classics of variational analysis. But in the available
proofs of almost all main results, fairly nontrivial as they are, techniques of
variational analysis do not play a significant part. In the paper we develop a
new approach that allows to obtain some generalizations of the the mentioned
results without invoking anything beyond elementary geometry of convex
polyhedra and some basic facts of the theory of metric regularity.
