We show how to model and verify a concurrent program using the Coq proof assistant. The program in question is an existing mail server written in Java. The approach we take is to use an original library that provides a language for modeling, a logic, and lemmas for verification of concurrent programs. First, we report on the modeling of the mail server. Using the language provided by the library, we build a model by (1) translating the original program and (2) building appropriate abstractions to model its environment. Second, we report on the verification of a property of the mail server. We compare this library-based approach with an alternative approach that directly appeals to the Coq language and logic for modeling and specification. We show that the library-based approach has many advantages. In particular, non-functional aspects (communications, non-determinism, multi-threading) are handled directly by the library and therefore do not require complicated modeling. Also, the model can be directly run using existing compilers or virtual machines, thus providing us with a certified implementation of the mail server.