Combined Heat and Power (CHP) generation units based on intermediate temperature (600-800°C) solid oxide fuel cell (SOFC) modules have been collaboratively developed by Mitsubishi Materials Corporation and The Kansai Electric Power Co., Inc. Currently, hydrocarbon fuel utilising units designed to produce modular power outputs up to 10 kWe-AC with overall efficiencies greater than 80%(HHV) are being tested. A unique seal-less stack concept is adopted to build SOFC modules accommodating multiple stacks incorporated of stainless steel separators and disk-type planar electrolyte-supported cells. In order to advance the current technology to achieve improved levels of efficiency and reliability, through design iterations, computational modelling tools are being heavily utilised. This contribution will describe the results of coupled computational fluid dynamics (CFD) analysis performed on our fourth-generation l kW class SOFC stack. A commercially available CFD code is employed for solving the governing equations for conservation of mass, momentum and energy. In addition, a local electrochemical reaction model is coupled to the rest of the transport processes that take place within the SOFC stack. It is found that the CFD based multi-physics model is capable of providing necessary and proper guidance for identifying problem areas in designing multi-cell SOFC stacks. The stack performance is also estimated by calibrating the computational model against data obtained by experimental measurements.