Conventional session type systems guarantee progress within single sessions, but do not usually take into account the dependencies arising from the interleaving of simultaneously active sessions and from session delegations. As a consequence, a well-typed system may fail to have progress, even assuming that helper processes can join the system after its execution has started. In this paper we develop a static analysis technique, specified as a set of syntax-directed inference rules, that is capable of verifying whether a system of processes engaged in simultaneously active multiparty sessions has the progress property.