Stellar winds are typical features of the AGB evolution. They are formed as the result of the radiation pressure on dust grains. We calculate the radiation pressure force of a red giant acting on prolate and oblate spheroidal grains of different size, aspect ratio and chemical composition. The exact solution to the light scattering problem for spheroids is used. The force and the grain drift velocity (relative to gas) are compared for spheroids and spheres of the same volume. It is found that for small spheroids (radii of equivolume sphere r_V ≲ 0.1 μm) the radiation pressure force usually is greater than that for spheres. A very significant effect occurs for strongly absorbing particles with r_V ≲ 0.03-0.05 μm. It is caused by the resonance absorption of incident radiation whose electric vector is parallel to the major axis of a particle. As a result, the velocity of a sphere and equivolume spheroid of iron can differ in 5 - 10 times or more. Another effect is the deviations of the radiation pressure force from the direction of the wave-vector of incident radiation. This is due to an azimuthal asymmetry of geometry of light scattering by non-spherical particles. The transversal component of the force is more important for dielectric particles and can reach up to 30 - 50% of the radial one for silicate grains of the size r_V ≈ 0.3 μm. It should increase the path of non-spherical grains in stellar envelopes and the number of dust-gas collisions in the comparison with spherical grains. The tendency of a strengthening of the radial component of the radiation pressure force and a weakness of the transversal one with a decrease of the stellar effective temperature is noted.