This paper describes a model using boundary element and finite element methods for the solution of three-dimensional incompressible viscous flows in slow motion, using velocity-vorticity variables. The method involves the solution of diffusion-advection type vorticity equations for vorticity whose solenoidal vorticity components are obtained by solving a Poisson equation involving the velocity and vorticity components. The Poisson equations are solved using boundary elements and the vorticity diffusion type equations are solved using finite elements and both are combined. Here the results of Stokes flow with very low Reynolds number, in a typical cavity flow are presented and compared with other model results. The combined BEM-FEM model has been found to be efficient and satisfactory.