This paper addresses the problem of evaluating the Web service quality using Finite State Machines. The most popular metrics for estimating such quality and user perception are Quality of Service (QoS) and Quality of Experience (QoE), which represent objective and subjective assessments, correspondingly. In this paper, we show how QoS can be estimated for Web services and their composition using finite state models. We also discuss how different machine learning algorithms can be applied for evaluating QoE of Web services based on known QoS parameter values