The development of trustworthy self-stabilizing algorithms requires the verification of some key properties with respect to the formal specification of the expected system executions. The atomic-state model (ASM) is the most commonly used computational model to reason on self-stabilizing algorithms. In this work, we propose methods and tools to automatically verify the self-stabilization of distributed algorithms defined in that model. To that goal, we exploit the similarities between the ASM and computational models issued from the synchronous programming area to reuse their associated verification tools, and in particular their model checkers. This allows the automatic verification of all safety (and bounded liveness) properties of any algorithm, regardless of any assumptions on network topologies and execution scheduling.