We propose a deterministic bicriteria model for stochastic variational inequalities based on some existing deterministic models. We reformulate the bicriteria model into a single objective problem involving a conditional value-at-risk (CVaR) term and introduce two approximation methods for solving the single objective problem, which are based on the primal and dual formulations of CVaR, respectively. In particular, for the primal problem, we introduce a smooth approximation of CVaR and establish some properties for this approximation problem. Then, we use sample average approximation methods to deal with the single objective problem and investigate the limiting behaviors of optimal solutions and stationary points. For the dual problem, we regularize the inner maximization problem and demonstrate the convergence of the approximation.