Abstract We give a semantics for Message Flow Graphs (MFGs), which play the role for interprocess communication that Program Dependence Graphs play for control flow in parallel processes. MFGs have been used to analyse parallel code, and are closely related to Message Sequence Charts and Time Sequence Diagrams in telecommunications systems. Our requirements are firstly, to determine unambiguously exactly what execution traces are specified by an MFG, and secondly, to use a finite-state interpretation. Our methods function for both asynchronous and synchronous communications. From a set of MFGs, we define a transition system of global states, and from that a Büchi automaton by considering safety and liveness properties of the system. In order easily to describe liveness properties, we interpret the traces of the transition system as a model of Manna-Pnueli temporal logic. Finally, we describe the expressive power of MFGs by mimicking an arbitrary Büchi automaton by means of a set of MFGs.