This paper presents a new contribution to the model-checking of multithreaded programs with recursive procedure calls, result passing between recursive procedures, dynamic creation of parallel processes, and synchronisation between parallel threads. To represent such programs accurately, we define the model SPAD that can be seen as the extension with synchronisation of the class PAD (the subclass of the rewrite systems PRS where parallel composition is not allowed in the lefthand sides of the rules). We consider in this paper the reachability problem of this model, which is undecidable. As in [BET03a,BET04], we reduce this problem to the computation of abstractions of the sets of execution paths of the program, and we propose a generic technique that can compute different abstractions (of different precisions and different costs) of these sets.