In this paper, loss probabilities and steady state probabilities of data packets for an asynchronous transfer mode (ATM) network are investigated under the buffer division and push-out schemes. Data packets are classified in classes k which arrive in Poisson fashion to the service facility and are served with general service rate under buffer division scheme, finite buffer space N is divided in to N1, N2, …, Nk such that N= N1+ N2 +…+ Nk. Under push-out scheme if upon arrival of class 1 packet to the system finds that there are less than N1-1 class 1 packets waiting for service and there is no unoccupied buffer space then one of the packets of other classes is pushed out. The pushed out packet is lost. The packets are served under general service discipline.