An axisymmetric boundary element method has been used to simulate primary atomization of a liquid jet including the effects of the orifice passage geometry. A ring vortex is placed at the orifice exit plane; its strength and location are uniquely determined by the local boundary layer characteristics at this locale. Using this methodology, nonlinear simulations are performed that include hundreds of individual atomization events. A linear analysis due to Ponstein is used to estimate the number of droplets formed from individual rings of fluid which are pinched from the periphery of the jet. Numerous results have been obtained to assess the effects of fluid parameters and orifice design on droplet sizes and atomization characteristics. Predicted droplet sizes show agreement with some limited experimental data.