Comparisons are made between the results of the buckley-leverett and kern solutions, which describe immiscible displacement of oil by gas in a linear system and the results obtained from a less restrictive numerical model. This model takes into account the effect of compressibility of the oil and gas and the effect of allowing changes in the amount of gas in solution in the oil. These effects are best exemplified by imposing large pressure drops across the system. With these large pressure drops, comparison of the model solution with the buckley-leverett solution reveals that the buckley- leverett solution provides estimates of recoveries at breakthrough of the gas that are too low. In contrast to the model, the kern solution predicts breakthrough recoveries that are too high. A modification to the kern solution is presented to facilitate more accurate predictions of recovery at gas breakthrough for gas injection at pressures higher than the saturation pressure of the oil.