In this paper, a three dimensional numerical model to simulate the steady state heat transfer and fluid flow of a flat-tube high power density solid oxide fuel cell (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 flat-tube HPD-SOFC are investigated. The variation of the temperature and flow fields with the current output is studied The simulation also predicts pressure drop behavior of the both the air and fuel streams. This heat transfer and fluid flow modeling of the computer code 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.