We present in this paper a new approach to the static analysis of concurrent programs with procedures. To this end, we model multi-threaded programs featuring recursive procedure calls and synchronisation by rendezvous between parallel threads with communicating pushdown systems (from now on CPDSs). The reachability problem for this particular class of automata is unfortunately undecidable. However, it has been shown that an efficient abstraction of the execution traces language can nonetheless be computed. To this end, an algebraic framework to over-approximate context-free languages has been introduced by Bouajjani et al. In this paper, we combine this framework with an automata-theoretic approach in order to approximate an answer to the model checking problem of the lineartime temporal logic (from now on LTL) on CPDSs. We then present an algorithm that, given a single-indexed or stutter-invariant LTL formula, allows us to prove that no run of a CPDS verifies this formula if the procedure ends.