Since multi-stack models are generally Turing-complete, verification problems on general models for asynchronous communication programs are undecidable. This paper proposes a new model based Petri net, named communication Petri nets (C-Petri nets) to model asynchronous communication programs. Applying the k-shaped restriction on the input communications and the abstraction on each stack based on popping lemma of regular languages, the coverability problem of the restricted C-Petri net is decidable by encoding the model to data Petri nets.