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. A detailed study was employed to predict the two-stroke direct injection linear engine behavior over a wide operating range, given intake parameters, variation in fuel to air ratio, reciprocating assembly mass, friction load, injection timing, and bore to stroke dimensions as some of the parameters used in the study. It was found that the operating frequency was relatively insensitive to reciprocating mass: for example, with other control variable fixed, a change in mass from 2kg to 7kg reduced frequency from 73Hz to 48Hz. Operating efficiency is also insensitive to most parameters, changing only 0.8% over a range of operating frequencies from 56Hz to 73Hz.