We propose to include the vehicle body sway motion into the motion planning of a quadruped's wave gaits such that its stability margin can be substantially increased. Two sway motions are proposed: Y-sway and E-sway. The Y-sway motion is simple, which drives the center of gravity (CG) of the vehicle to approach to the y-component of the geometric center of the contact points of the supporting legs. The E-sway motion drives CG to approach to the desired CG locus for considering equal energy stability levels. Both sway motions are reasonably easy to implement. Between them, the E-sway can achieve better stability margin. When sloped terrains are encountered, body tilt is also considered in the initialization phase to improve the stability margin. Simulation results show that the body sway motions and tilt consideration are not mutually exclusive. Therefore, we may combine both actions to further increase the stability margin.