A finite‐difference solution is developed to study the two‐dimensional flowfields of a combustion chamber. The methodology is also applied to the steady in‐cylinder flows, where the boundary of the cylinder head is a curved wall. The curved wall is described by a cubic spline interpolation function. The governing equations are expressed in axisymmetric nonorthogonal curvilinear coordinates. A rectangular computational domain is yielded by Moretti's transformation and the task of numerically generating the body‐fitted coordinates is avoided. Hence, the matrix of the coordinate transformation can be determined by direct analytic differentiation. The discretized conservation equations are derived on a control volume basis and solved by the extended SIMPLE calculation procedure. The program is run on an IBM PC/AT. Numerical results obtained by employing the present methodology are compared with results from an analytical solution. The relative merits of three numerical representations, i.e., power‐law, hybrid and first‐order upwind, for approximating the convection terms in the momentum equations are compared. The application of the methodology is illustrated using steady in‐cylinder flows. The effects of inlet Reynolds number on the velocity distribution are also investigated.