Steady state three-dimensional incompressible flow analysis based on the two-equation model of turbulence is performed. The finite element method employing the penalty function formulation by Hughes et al. (1979) is used. To reduce the computational time and computer storage, the conjugate gradient method is applied to solve algebraic equations. In applying the conjugate gradient method, the equations are preconditioned so as to arrive at converged solutions effectively. The problem cited in this study is the impingement air cooling of the large scale integrated circuit package with large plate fins. The calculated velocity vectors show good agreement with the result of flow visualization. The calculated temperature distributions also agree well with the experimental temperatures. This suggests the usefulness of this kind of numerical simulation in the research and development of new cooling technologies.