In this paper, we analyzed the packet blocking probability of a finite buffer in a network interface unit. In general, a network interface unit which provides a means of interface between the network and computer has a microprocessor and a protocol processor for the network access protocols. It also has a receive buffer for the arriving packets from the network which is served by the microprocessor with service interruption by the protocol processor. In this paper, we modeled the receive buffer as a discrete time server with service interruption, and obtained the packet blocking probability using the mini-slot approximation.