The transient behavior of the jet emerging from the orifice during the start-up and shut-down portion of a typical high-pressure diesel-engine fuel injection is addressed in the present work. The liquid jet injected into air at high pressure has been simulated during start-up, steady-state, and shut-down. Use has been made of an unsteady axisymmetric code with a finite-volume solver of the Navier-Stokes equations for liquid streams and adjacent gas, a boundary-fitted-gridding scheme, and a level-set method for liquid/gas interface tracking. Full jet calculations and analysis have been made. In addition, to ease the resolution problem and capture the shortest unstable surface wavelengths, a new model has been developed to examine stream-wise segments of the jet during transients. The frame of reference has been transferred from the laboratory frame to an accelerating frame fixed to the liquid. This transformation generates a new term as a generalized body force analogous to gravity in equations of motion. Periodic conditions before and aft of the segment are used in this liquid-segment model. Consistent results follow from the two approaches. The acceleration of the liquid during start-up is about 106 m/s2 at the orifice exit for high Reynolds numbers. When the jet emerges from the orifice, drag forces due to the dense ambient air cause a deceleration. The classical mushroom cap for the developing jet is shredded and non-existent at high Reynolds number. Also, the dynamic protrusions from the jet surface created by shear instability are subject to local accelerations that lead to Rayleigh-Taylor (RT) instability. The higher the Weber and the Reynolds numbers, the shorter the unstable surface wavelengths which appear; so, the more challenging is the resolution problem. Effects of the acceleration, surface tension, and liquid viscosity on the interface instability have been investigated.