Interfacial instability plays an important role in the primary atomization of high-speed liquid jets. We present simulations of the Kelvin-Helmholtz instability of a sheared liquid-gas interface. The two-dimensional simulations of the Navier-Stokes equation with surface tension show good agreement with a new linear theory in the region of exponential growth. Beyond that regime the formation of liquid sheets is observed at sufficiently high Weber and Reynolds numbers. Three-dimensional simulations show the formation of streamwise liquid fingers for a high level of three dimensionality in the initial conditions. This scenario involves a faster distortion of the rim; the precise mechanism that yields this behavior is still unknown.