The analysis of software architecture plays an important role in understanding the system structures and facilitate proper implementation of user requirements. Despite its importance in the software engineering practice, the lack of formal description and verification support in this domain hinders the development of quality architectural models. To tackle this problem, in this work, we develop an approach for modeling and verifying software architectures specified using Monterey Phoenix (MP) architecture description language. MP is capable of modeling system and environment behaviors based on event traces, as well as supporting different architecture composition operations and views. First, we formalize the syntax and operational semantics for MP; therefore, formal verification of MP models is feasible. Second, we extend MP to support shared variables and stochastic characteristics, which not only increases the expressiveness of MP, but also widens the properties MP can check, such as quantitative requirements. Third, a dedicated model checker for MP has been implemented, so that automatic verification of MP models is supported. Finally, several experiments are conducted to evaluate the applicability and efficiency of our approach.