The problem of flow around a marine propeller performing a general 3D unsteady motion in an infinitely extended fluid is formulated and solved using a boundary element method. Hydrodynamic modeling of the freely moving—unsteady—trailing vortex sheet emanating from each blade is achieved, using vortex filaments and a time stepping method. Thus vortex wake–blade interaction can be taken correctly into consideration. The method uses bilinear panels for the representation of blade and free wake geometry and constant panels for the representation of the unknown dipole intensity. The proposed method produces very stable rollup wake patterns for both steady and unsteady problems for a broad range of discretization parameters. Application of the method to a number of specific cases of steady and unsteady propeller motion has shown the very good numerical performance of the method and that good predictions for forces and pressure distributions can be obtained.