This paper describes an iterative dual reciprocity boundary element method (DRBEM) for the solutions of Stokes and Navier-Stokes equations in cavities under the effect of an external point source magnetic field placed very close to the bottom. The fluid is viscous, incompressible and electrically non-conducting but magnetizable, and the flow is steady, laminar and fully developed. Both the Stokes and Navier-Stokes equations are solved in terms of velocity and pressure of the fluid by using DRBEM. Pressure boundary conditions are obtained through momentum equations by approximating pressure gradients with finite differences. All the space derivatives are computed by using DRBEM coordinate matrix. The results of Stokes flow under point magnetic source in lid-driven square and circular cavities are presented and compared. The three-dimensional flow of an incompressible fluid is considered in the 2D rectangular cross-section of a long duct with and without a moving top-lid imposed to a point magnetic source. The axial velocity is also computed due to the pressure gradient given in the axial direction. The obtained results for varying magnetic number show that the flow is appreciably influenced by the presence of the magnetic field. (C) 2015 Elsevier Ltd. All rights reserved.