In this paper, a new hybrid Mode Matching- Finite Element-Spectral Decomposition (MM-FE-SD) approach applied to the analysis of finite large arrays is presented. In particular, the MM-FE is applied to the analysis of an infinite phased array of rectangular waveguides feeding arbitrary shaped thick irises. The SD approach allows us to properly combine the results obtained in the case of the infinite array in order to take into account the finite size of the array. Representative numerical examples are shown to demonstrate the effectiveness of the method.