We analyze the sensitivity of parameterized variational inequalities for co
nvex polyhedric sets in reflexive Banach spaces. We compute a generalized d
erivative of the solution mapping where the formula for the derivative is g
iven in terms of the solutions to an auxiliary variational inequality. Thes
e results are distinguished from other work in this area by the fact that t
hey do not depend on the uniqueness of the solutions to the variational ine
qualities. To obtain our results, we use second-order epi-derivatives to an
alyze the second-order properties of polyhedric sets. We apply our results
to sensitivity analyses of stationary points and KKT pairs associated with
constrained infinite-dimensional optimization problems.