Currently, Service-Oriented Architecture (SOA) is becoming the most popular software architecture of contemporary enterprise applications, and one crucial technique of its implementation is web services. Individual service offered by some service providers may symbolize limited business functionality; however, by composing individual services from different service providers, a composite service describing the intact business process of an enterprise can be made. Many new standards have been defined to decipher web service composition problem namely Business Process Execution Language (BPEL). BPEL provides an initial work for forming an Extended Markup Language (XML) specification language for defining and implementing business practice workflows for web services. The problems with most realistic approaches to service composition are the verification of composed web services. It has to depend on formal verification method to ensure the correctness of composed services. A few research works has been carried out in the literature survey for verification of web services for deterministic system. Moreover the existing models did not address the verification properties like dead transition, deadlock, reachability and safetyness. In this paper, a new model to verify the composed web services using Enhanced Stacked Automata Model (ESAM) has been proposed. The correctness properties of the non-deterministic system have been evaluated based on the properties like dead transition, deadlock, safetyness, liveness and reachability.Initially web services are composed using Business Process Execution Language for Web Service (BPEL4WS) and it is converted into ESAM (combination of Muller Automata (MA) and Push Down Automata (PDA)) and it is transformed into Promela language, an input language for Simple ProMeLa Interpreter (SPIN) tool. The model is verified using SPIN tool and the results revealed better recital in terms of finding dead transition and deadlock in contrast to the existing models.