CFD (computational fluid dynamics) theory such as equations of conservation and of the turbulent kinetic energy are explained along with their numerical solution and the FIRE solution algorithm. The techniques are applied to different areas of four-stroke and two-stroke engines such as to a small 4-valve engine with moving piston and moving valves and different intake ports to show the in-cylinder charge movement, followed by the flow calculation and heat transfer in the water jacket and applied also to detect the velocity pattern on the front face of the catalyst, all in the same 150cc engine. One of the CFD applications to different two-stroke engines deals with the variation of manifold-diffuser-catalyst layouts to obtain an evenly distributed velocity in the catalyst. Second a fan cooling system with rotating fan indicates the weaknesses of the original layout in terms of cylinder temperature distribution and improvement steps are shown. The final chapter deals with a 125cc two-stroke engine modeled from reed valve to exhaust tailpipe including crankcase with rotating crankshaft and moving piston along with a complete resonance exhaust system. Results are shown for full load at rated speed and for part throttle at medium engine speed.