Numerical simulations are used to study an under-expanded sonic jet injected into a supersonic crossflow and an over-expanded supersonic jet injected into a subsonic crossflow. A finite volume compressible Navier - Stokes solver developed by Park & Mahesh (2007) for unstructured grids is used. The flow conditions are based on Santiago et al.'s (1997) and Beresh et al.'s (2005) experiments for sonic and supersonic injection, respectively. The simulations successfully reproduce experimentally observed flow vortical structures and shock systems such as the barrel shock, Mach disk, horseshoe vortices that wrap up in front of the jet and the counter rotating vortex pair (CVP) downstream of the jet. The time averaged flow fields are compared to the experimental results, and reasonable agreement is observed.