This paper presents a multi-physical dynamic fuel cell stack model. This model covers three major physical domains: electrical, fluidic and thermal. The dynamic model in each domain is presented. The fuel cell stack model is obtained by stacking method from a generalized single cell model, thus the spatial effect through the stack can be modelled and observed. The stack model is validated temporally and spatially against a Ballard NEXA 1.2 kW 47 cells fuel cell stack. Then, the dynamic behaviour in each physical domain is analysed. It can be approximated by a first order system, thus the expressions of time constants in different domain are obtained. Finally, the fuel cell stack spatial non-homogeneity is analysed. From the results, a fuel cell stack model reduction method is proposed in order to reduce the computation time during simulations. The reduced fuel cell stack model is validated against the full model.