This paper presents two equivalent analytical models to study the performance of finite queuing systems with Erlangian network services. Erlangian services are commonly seen in the processing of received network packets by many network servers. Our models allow us to derive equations for key features and performance measures of engineering and design significance. These features and measures include throughput, packet loss, packet delay, and server CPU availability. Numerical examples are given to study the performance while varying the number of service stages and the size of finite buffer. Discrete-event simulation has been used to verify the proposed analytical models.