Distributed memory machines (DMMs) can provide scalable and flexible high performance if the relatively high startup overhead on these machines can be amortised. This paper studies communication overhead on DMMs. Based on LogP, a communication cost model is developed to quantify separately the effects of send, receive and network contention on overall communication overhead. This cost model is applied to estimate communication overhead for four commercial multicomputer systems. Two observations for send and receive overheads on DMMs are discussed.