The critical nature of many complex software-intensive systems calls for formal, rigorous architecture descriptions as means of supporting automated verification and enforcement of architectural properties and constraints. Model checking has been one of the most used techniques to automatically analyze software architectures with respect to the satisfaction of architectural properties. However, such a technique leads to an exhaustive exploration of all possible states of the system under verification, a problem that becomes more severe when verifying dynamic software systems due to their typical non-deterministic runtime behavior and unpredictable operation conditions. To tackle these issues, we propose using statistical model checking (SMC) to support the analysis of dynamic software architectures while aiming at reducing effort, computational resources, and time required for this task. In this paper, we introduce a novel notation to formally express architectural properties as well as an SMC-based toolchain for verifying dynamic software architectures described in π-ADL, a formal architecture description language. We use a flood monitoring system to show how to express relevant properties to be verified, as well as we report the results of some computational experiments performed to assess the efficiency of our approach.