We present a new model based on Monte Carlo ray tracing which simulates scattering and linear polarization by particles with arbitrary shapes and sizes much larger than the wavelength. The model, called S-Scat, provides a powerful tool for exploring the relationship between actual physical properties of large particles and the single-particle parameters used in multiple-scattering radiative transfer models, and will be particularly valuable for studies of icy outer solar system surfaces. We describe the model algorithm and apply the model to examine absorption and scattering behavior of single, irregular particles as functions of particle size, shape, and optical constants. Single-scattering albedos are investigated first, with results used to test the validity of the widely used equivalent slab model. Single-scattering phase functions are examined next, along with possibilities of parameterization via simple analytic expressions. Finally, the behaviors of linear polarization functions are explored, along with internal path lengths and the spatial distribution of scattered light in close proximity to the particle. ¿ 2000 American Geophysical Union