Unsteady gas flow theory can be used for simulating a spark ignition internal combustion engine’s exhaust system, using pressure waves. The method explained here is based on the discretization of interpolated spaces (called meshes) which are located throughout the whole length of the exhaust pipe, irrespective of its form or size. The most important aspects of this theory are theoretically explored, such as pressure wave movement and shock and their application to cases found in real engines’ exhaust pipes. This work also considers how the simulation must be made, based on the previous exploration. The results (presented as equations in this first paper) show the great influence exerted by pressure wave movement on flow through the engine and therefore on its final performance.