Many distributed systems use broadcast communication for various reasons such as saving energy or increasing throughput. However, the actor model for concurrent and distributed systems does not directly support this kind of communication. In such cases, a broadcast must be modeled as multiple unicasts which leads to loss of modularity and state space explosion for any non-trivial system. In this paper, we extend Rebeca, an actor-based model language, to support asynchronous anonymous message broadcasting. Then, we apply counter abstraction for reducing the state space which efficiently bypasses the constructive orbit problem by considering the global state as a vector of counters, one per each local state. This makes the model checking of systems possible without further considerations of symmetry. This approach is efficient for fully symmetric system like broadcasting environments. We use a couple of case studies to illustrate the applicability of our method and the way their state spaces are reduced in size.