The purpose of this study is to identify the potential locations for cavitation induced by total stress on the flow of a liquid through and orifice of an atomizer. A numerical simulation of two-phase incompressible flow is conducted in an axisymmetric geometry of the orifice for Reynolds number between 100 and 2000. The orifice has a rounded upstream corner and a sharp downstream corner with length-to-diameter ratio between 0.1 and 5. The total stress including viscous stress and pressure has been calculated in the flow field and , from there, the maximum principal stress is found. The total-stress criterion for cavitation is applied to find the regions where cavitation is likely to occur and compared with those of the traditional pressure criterion. Results show that the viscous stress has significant effects on cavitation. The effect of geometry and occurrence of hydraulic flip in the orifice on the total stress is studied. The Navier-Stokes equations are solved numerically using a finite-volume method and a boundary-fitted orthogonal grid that comes from the streamlines and potential lines of an axisymmetric equipotential flow in the same geometry. A level-set formulation is used to track the interface and model the surface tension.