Increasing deployment of computer systems in critical applications has made study and quantifiable analysis of these systems as an important issue. This analysis can either be done on real system or by developing analytic models. First approach is less desirable, since such an analysis is typically done in a post-facto manner after any problem has occurred. The modeling approach on the other hand, can be done in an a-prior manner and is also much less costly. In this paper an architecture for internet voting system based on dependable web services is described as our case study. Dependability attributes are applied to this system as one of the most important specifications of critical systems. On the other hand voting requirements is considered in this architecture. After explaining the architecture it is modeled with RBD and Petri nets. Then these models are evaluated and reliability, availability and system failure is calculated quantitatively. By using these quantitative results, we can understand whether the system which is going to be created based on this model, will address our requirements or not.