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Research at West Virginia University has led to the development of a novel crankless reciprocating internal combustion engine. This paper presents a time-based model used to investigate the performance of two-stroke direct injection compression ignition linear engines. The two-stroke linear engine consists of two pistons, linked by a connecting rod, that are allowed to move freely in response to changes in the engine's fueling and load across the full operating cycle of the engine. The computer model uses a combination of a series of dynamic and thermodynamic numerical equations, which have been solved to provide a detailed analysis of the two-stroke direct injection linear engine operation. Parameters such as rate of combustion, convection heat transferred inside the cylinders, friction forces, external loads, acceleration, velocity profile, compression ratio, and in-cylinder pressures were modeled.