In this paper, a model for the radiation force exerted by standing surface acoustic waves (SSAWs) on a rigid cylinder in inviscid fluids is extended to account for the dependence on the Rayleigh angle. The conventional model for the radiation force used in the SSAW-based applications is developed in plane standing waves, which fails to predict the movement of the cylinder in the SSAW. Our revised model reveals that, in the direction normal to the piezoelectric substrate on which the SSAW is generated, acoustic radiation force can be large enough to drive the cylinder even in the long-wavelength limit. Furthermore, the force in this direction can not only push the cylinder away, but also pull it back toward the substrate. In the direction parallel to the substrate, the equilibrium positions for particles can be actively tuned by changing Rayleigh angle. As an example considered in the paper, with the reduction of Rayleigh angle the equilibrium positions for steel cylinders in water change from pressure nodes to pressure antinodes. The model can thus be used in the design of SSAWs for particle manipulations.