To both increase the power density of a tubular solid oxide fuel cell (SOFC) and maintain its beneficial feature of secure sealing, a flat-tube high power density (HPD) solid oxide fuel cell is under development by Siemens Westinghouse, based on their formerly developed tubular model. In this paper, a three dimensional numerical model to simulate the steady state heat transfer and fluid flow of a flat-tube HPD–SOFC is developed. A computer code is programmed using the FORTRAN language to solve the governing equations for continuity, momentum, and energy conservation. The highly coupled temperature and flow fields of the air stream and the fuel stream inside and outside a typical channel of a one-rib flat-tube HPD–SOFC are investigated. This heat transfer and fluid flow results will be used to simulate the overall performance of a flat-tube HPD–SOFC in the near future, and to help optimize the design and operation of a SOFC stack in practical applications.