The present work is devoted to the study of cryogenic nitrogen jets in sub- and supercritical conditions. A general trend to operate under increasingly higher combustor pressures is observed in rockets, gas turbines, and diesel engines, primarily as a result of enhanced effects on thrust, power, or efficiency. In these conditions the injected fluid(s) can experience ambient pressures exceeding the critical pressure(s) of the propellants, and recent experimental work of Chehroudi et al. showed a quantitative similarity to gas-jet-like behavior (Chehroudi, B., Cohn, R., and Talley, D., Spray/Gas Behaviour of Cryogenic Fluids under Sub- and Supercritical Conditions, Paper, July 2000; Chehroudi, B., Cohn, R., and Talley, D., Initial Growth Rate and Visual Characteristics of a Round Jet into a Sub- to Supercritical Environment of Relevance to Rocket, Gas Turbine, and Diesel Engines, AIAA Paper 99-0206, Jan. 1999). This conclusion suggested that it would be expected that the mathematical models and numerical methods used for gaseous flows could also be used for supercritical flows. This paper reports an investigation, exploring this hypothesis, and aims to evaluate the capabilities and limitations of a computational method developed for incompressible but variable density flows when applied to supercritical conditions. The predicted initial jet growth rate was compared with available experimental data for liquid/gaseous jets and mixing layers and showed a good agreement for different supercritical density ratios. For subcritical conditions, when the flow deviates from the gaseous-like behavior, and approaches a more spray-like behavior the incompressible gaseous flow formulation was found inadequate.