We have calculated the radiation pressure force acting on prolate and oblate spheroidal grains of different size, aspect ratio, chemical composition and alignment. The consideration has been done for conditions typical of the envelopes of carbon-rich or oxygen-rich giants. The force and the grain drift velocity (relative to gas) obtained as a solution of simple equation of dust motion have been compared for spheroids and spheres of the same volume.
It is found that for spheroids with radii of equivolume sphere
the radiation pressure force commonly
is greater than that for spheres.
The effect is in particular strong for highly absorbing particles with
.
It is explained 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 spheroids consisting
of iron can differ in 
times or more.
Another effect is the existence of the component of the radiation
pressure force perpendicular to the wave-vector in the case of oblique
incidence of radiation. It is caused by an azimuthal asymmetry
of geometry of light scattering by non-spherical particles.
The transversal component of the force is prominent for
dielectric particles and can reach up to 
% of the radial one
for silicate grains of the size 
.
This component should increase the path of non-spherical grains
and the number of their collisions with the gas particles
in the envelopes of late-type stars.
Such an effect can enlarge the living time of
silicate grains in the envelopes that may facilitate the process
of crystallization of amorphous silicates.
The grain porosity generally decreases both radial and transversal
components of the radiation pressure force if the particles of the
same volume are considered. For silicate grains, this reduction
appears for aggregates containing more than 
% of vacuum.
Variations of the effective temperature of the stars can lead to a strengthening of the radial component of the radiation pressure force during brightness minima and of the transversal one during maxima.
Acknowledgements
The authors are thankful to R. Stognienko for comments. V.B.I. acknowledges the Alexander von Humboldt Foundation for the financial support. The work was partly supported by the Committee of High Education for Russian Federation (grant 95-0-3.1-1).