Multiple scattering of incoherent polarized light propagating through a ran
dom medium comprised of spheroidal Rayleigh particles is studied using Mont
e Carlo simulations. Two approaches are taken for the implementation of the
simulation: the first uses individual realizations of particle orientation
and the second, an accelerated method, averages over the particle orientat
ion. These different methods produce results that are indistinguishable wit
hin statistical errors. The depolarization of light is examined in both tra
nsmission and backscatter for media comprised of spheroids of different pol
arizability ratios. In media containing spheroidal particles the depolariza
tion is greater than that for spherical particles. Media containing prolate
spheroids are more depolarizing than media comprising oblate particles of
the same polarizability ratio. The extra depolarization due to asphericity
is much less pronounced in the multiple scattering regime than for single s
cattering.