A theoretical model to simulate the gas exchange process in a two-stroke, cross or loop-scavenged engine is presented. In this model, the geometry of the cylinder and port assemblies, as well as the physical conditions of operation are represented. The mathematical model consists of five conservation laws in quasi 3-dimensional form. These were transformed into a form which both allows the domain of solution always to be confined in the volume occupied by the gas and also fits the geometry of the cylinder ports. The transformed equations were solved numerically by a finite-difference method to yield the instantaneous and spatial distribution of the temperature, gas composition and velocity fields inside the cylinder from which the gas exchange process was characterized. The predictions were compared with some experimental observations obtained from a flow visualization rig and found in good agreement.