This paper reports on the simulations of a round jet issuing vertically into a crossflow by a three-dimensional vortex filament method. The flow is modeled by a series of vortex rings emitted from the jet source. The mechanism of the formation of counter-rotating vortex pair is presented : the lateral sides of each vortex ring are strongly stretched in the axial direction of jet and coalesce into two line vortices. The vortex hairpin removal algorithm proposed by Chorin (1993) is partially implemented and its effectiveness is preliminarily investigated.