This paper presents an approach to verify safety properties of Erlang-style, higher-order concurrent programs automatically. Inspired by Core Erlang, we introduce λActor, a prototypical functional language with pattern-matching algebraic data types, augmented with process creation and asynchronous message-passing primitives. We formalise an abstract model of λActor programs called Actor Communicating System (ACS) which has a natural interpretation as a vector addition system, for which some verification problems are decidable. We give a parametric abstract interpretation framework for λActor and use it to build a polytime computable, flow-based, abstract semantics of λActor programs, which we then use to bootstrap the ACS construction, thus deriving a more accurate abstract model of the input program. We evaluate the method which we implemented in the prototype Soter. We find that in practice our abstraction technique is accurate enough to verify an interesting range of safety properties. Though the ACS coverability problem is Expspace-complete, Soter can analyse non-trivial programs in a matter of seconds.