This paper considers a class of two-stage stochastic linear variational inequality problems whose rst stage problems are stochastic linear boxconstrained variational inequality problems and second stage problems are stochastic linear complementary problems. We rst give conditions for the existence of solutions to both the original problem and its perturbed problems. Next we derive quantitative stability assertions of this two-stage stochastic problem under total variation metrics via the corresponding residual function. After that, we study the discrete approximation problem. The convergence and the exponential rate of convergence of optimal solution sets are obtained under moderate assumptions respectively. Finally, through solving a noncooperative two-stage stochastic game of multi-players, we numerically illustrate the obtained theoretical results.