Automated reasoning tools for security protocols model protocols as non-deterministic processes that communicate through a Dolev-Yao attacker. There are, however, a large class of protocols whose correctness relies on an explicit ability to model and reason about randomness. Although such protocols lie at the heart of many widely adopted systems for anonymous communication, they have so-far eluded automated verification techniques. We propose an algorithm for reasoning about safety properties for randomized protocols. The algorithm is implemented as an extension of Stochastic Protocol ANalyzer (Span), the mechanized tool that reasons about the indistinguishability properties of randomized protocols. Using Span, we conduct the first automated verification on several randomized security protocols and uncover previously unknown design weaknesses in several of the protocols we analyzed.