An advanced computational fluid dynamics package, REFLEQS, has been adapted to calculate the flow in the induction system of an internal combustion engine. Results of complex flow fields in multi-valve engine intake/exhaust ports and cylinders, including moving valves and piston, are calculated. The body-fitted structured grids generated with partial differential equations method have been applied to represent complex engine components configuration such as engine intake/exhaust ports, ducts, valves and cylinders. An upwind scheme combined with SIMPLEC method is employed to solve the Navier-Stokes equations. Several 2D and 3D flows in engine ports/cylinders are simulated. Complex flow fields involve separated flows near the entry of cylinder head, vortices near the corner and behind the valves and the valve/stem generated swirling and tumbling flows. The present work aims at establishing a generalized computational environment for analyzing the physical mechanisms and design parameters controlling internal flows in automotive air/fuel induction systems.