On the basis of the vector radiative transfer equation, multiple scattering calculations were performed for an obliquely incident linearly polarized plane wave upon a plane-parallel slab consisting of arrays of vertically oriented, uniformly distributed nonspherical spheroidal particles of identical size. Results are given in terms of the Stokes' parameters for the incoherent field. Owing to the symmetry of the particles and their orientation, decoupling of the Fourier expansion coefficients in the solution of the radiative transfer equation occurs. Each Fourier component satisfies a single equation which is then solved by the Gauss' quadrature and the eigenvalue-eigenvector technique. The behavior of the forward scattered incoherent field is investigated for low-loss as well as high-loss particles, for different densities and shapes, and for various angles of incidence. Comparison with the results from the approximate first-order theory shows good quantitative agreement for thin and sparcely populated layers.