The Stochastic CSP (SCSP) is a framework recently introduced by Walsh to capture combinatorial decision problems that involve uncertainty and probabilities. The SCSP extends the classical CSP by including both decision variables, that an agent can set, and stochastic variables that follow a probability distribution and can model uncertain events beyond the agent's control. So far, two approaches to solving SCSPs have been proposed; backtracking-based procedures that extend standard methods from CSPs, and scenario-based methods that solve SCSPs by reducing them to a sequence of CSPs. In this paper we further investigate the former approach. We first identify and correct a flaw in the forward checking (FC) procedure proposed by Walsh. We also extend FC to better take advantage of probabilities and thus achieve stronger pruning. Then we define arc consistency for SCSPs and introduce an arc consistency algorithm that can handle constraints of any arity.