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A semi-Lagrangian algorithm is associated with semi-implicit method in the integration of the shallow water equations. The resulting numerical algorithm is unconditionally stable. To obtain accurate results from a semi-Lagrangian integration scheme, it is necessary to choose the order of interpolation carefully. Cubic interpolation is used and it is a good compromise between accuracy and computational cost. The semi-Lagrangian semi- implicit scheme is applied to the shallow water equations with two kinds of boundary conditions, i.e. velocity component type or geopotential height type. When the boundary values are imposed on the velocity component some new relations are obtained using governing equations to solve geopotential height equation numerically. The integral invariants of the shallow water equations, i.e., mass, total energy and enstrophy are well conserved, ensuring that a realistic nonlinear structure is obtained.