With the rapid expansion of the Internet, Web servers have played a major role in accessing the enormous mass of Web pages to find the information needed by the user. Despite the exponential growth of the WWW, a very negligible amount of research has been conducted in Web server performance analysis with a view to improve the time a Web server takes to connect, receive, and analyze a request sent by the client and then sending the answer back to client. In this paper, we propose a multi-layer analytical approach to study the web server performance. A simple client-server model is used to represent the WWW server in order to demonstrate how to apply the proposed approach. We developed a systematic, analytical methodology to quantify the communication delay and queuing overhead in a distributed web server system. The approach uses the Computation Structure Model to derive server processing time required to process a request sent from a client and queueing model to analyze the communication between the clients and the server