Abstract: Grimshaw derived the rotation modified Kadomtsev-Petviashivili Equation (RKP Eq.) to discribe long surface or internal waves in the presence of rotation. The initial-boundary value problems of RKP equation are studied numerically in this paper. It is shown that solitary-like waves prapogating to the right can be found, whose amplitudes decay in the direction perpendicular to the direction of prapogation and the wave fronts are curvedback. The solitary waves remain unsteady and are always accompanied by Poincare waves travelling to the left.These effects are more noticeable as the effects of rotation are increased.