We describe a Monte Carlo method for calculating polorization due to s
cattering in various geometries. We apply the method in this paper to
the case of scattering in a spherical cloud illuminated by parallel ra
ys. The polarization is largest in small optical depth blobs, where si
ngle scattering dominates. The polarization decreases as optical depth
increases until a limit is reached where scattering occurs on the sur
face, and increasing optical depth has little effect on the results. F
or a given optical depth, decreasing the albedo leads to an increase o
f the degree of polarization of the scattered light because single sca
ttering increases relative to multiple scattering. As the optical dept
h of the blob increases, the scattered flux becomes increasingly backw
ard throwing. In the high albedo blobs, the maximum polarization becom
es skewed towards the illuminated hemisphere at high optical depths. W
e discuss the applications to polarization in supergaints and R CrB st
ars, and scattering in a clumpy interstellar medium.