Over recent decades many studies have emanated from The Queen's University of Belfast (QUB) regarding the modelling of the performance characteristics of the reciprocating internal combustion engine by following the unsteady gas flow in the ducting and through the cylinder. More recently, the author has published an ‘alternative’ method of modelling the unsteady flow in the engine ducting together with experimental proof of its accuracy for the simulation of two- and four-stroke cycle engines. Not only does the new model impose mass flow continuity at all sections of an engine and its ducting, but it is fully non-isentropic in its handling of friction, heat transfer and area changes along any duct. This paper presents a non-isentropic model of flow at a three way branch in a duct, which model expands significantly on previous theoretical approaches from QUB by its capabilities in dealing with mixtures of gases travelling through the branch. This is important for modelling all engines, but is especially so for the two-stroke cycle. The paper presents theoretical proof of these contentions by modelling significant elements of the exhaust systems of both two- and four-stroke engines and by a full engine simulation of a twin cylinder four-stroke engine.