This paper describes a modeling approach to compute the lumped parameter hydrodynamic derivative matrices of an underwater multi-hull vehicle. The vehicle, modeled as a multi-body underwater system and denoted as cluster, can be composed by heterogeneous bodies with known dynamic parameters, rigidly connected. The nonlinear dynamic equations of the cluster and its parameters are derived by means of a modular approach, based on the composition of single basic elements. The ultimate objective is to derive a mathematical description of the multi-hull system that captures its most significant dynamics allowing to design model-based motion controllers and navigation filters. The modular nature of the resulting model can be exploited, by example, when control reconfiguration is to be dealt with in the presence of (possibly multiple) failures. The numerical simulation of a hypothetical cluster is presented and discussed.