A low-order potential based boundary element method is applied to the prediction of the flow around the cavitating propeller in steady or in unsteady inflow. For given cavitation number, the cavity shape is determined in an iterative manner until the kinematic and the dynamic boundary conditions are both satisfied on the approximate cavity boundary. In order to improve the solution behavior near the tip region, a hyperboloidal panel geometry and a modified split panel method are applied. The method is then extended to include the analysis of time-varying cavitating flows around the propeller blades via a time-step algorithm in time domain. In the method, the steady state oscillatory solution is obtained by incremental stepping in the itme domain. Finally, the present method is validated through comparison with other numerical results and experimental data.