The numerical solution for the flowfield established in a spark- ignition internal combustion engine during the four-stroke (intake, compression, power, exhaust) cycle is considered. Only fluid-dynamic effects are treated with combustion simulated by constant- volume heat addition near top-dead-center on the compression stroke. The working fluid is assumed to be air of constant specific heat, with both viscous and inviscid models considered. Two- and three-dimensional engine models are examined, with the three-dimensional models including both rectangular and cylindrical geometries. The difficulties associated with obtaining numerical solutions in cylindrical coordinates for three-dimensional non-axisymmetric problems when the centerline is included in the region of interest are discussed. A new method which avoids the coordinate- singularity problems associated with such cases is presented and used to obtain the first known four-stroke inviscid-flow solution for a three- dimensional cylindrical engine model. Similar results are presented for a three-dimensional rectangular model, and for the first known two-dimensional four-stroke calculation for a viscous fluid. The inviscid three-dimensional results are compared with each other and with previously obtained two-dimensional inviscid-flow calculations. The use of two-dimensional models is found to be justified for the non- reacting flowfields considered, since the results obtained from a two-dimensional calculation in the valve plane are apparently not strongly dependent on the flowfield perpendicular to the valve plane. It is found that significant flowfields do exist in all I.C. engine models considered. It is shown that the unit-cell-Reynolds-number criterion limits viscous flow calculations to Reynolds numbers of approximately one ten-thousandth the realistic value, and that this produces flowfields which are strongly piston-dominated. In contrast, inviscid results show marked circulatory patterns, which are more realistic. The velocity patterns which develop in the three-dimensional cylindrical engine model are shown to exhibit a marked swirl in planes parallel and perpendicular to the cylinder axis.