Modeling the free surface flows is important in order to estimate the total drag of the sea Vessels. It is also necessary to study the effects of various maritime maneuvers. In this work, different ways of approximating an unstructured free surface grid with a B-spline surface are investigated. The Least squares and Galerkin approaches are studied in this regard. B-spline nite element method (BSPFEM) is studied for the solution of the steady-state kinematic free surface equation. The volume grid has to be moved in order to match the free boundary when the surface-tracking approach is adopted for the solution of free surface problem. Inherent smoothness of the B-spline representation of the free surface aids this process. B-spline representation of the free surface aids in building viscous volume grids hose boundaries closely match the steady state free surface. The B-spline approximation algorithm and BSPFEM solution of free surface equation have been tested with hypothetical algebraic testcases and real cases such as Gbody, Wigley hull and David Taylor Model Basin(DTMB) 5415 hull series.