Long-distance propagation of electromagnetic waves in weakly fluctuating random media often is described by radiative transfer equations (RTEs). RTEs find applications in subjects ranging from astrophysics to atmospheric science and remote sensing. Recently RTEs also have been used to model light propagation in diffusive biological tissue with application to optical imaging. Analytic solutions to the steady state RTE are limited to very simple sources and media. To use the equation for simulating realistic propagation phenomena, numerical methods are called for. This proposal seeks funding to develop a surface integral equation (SIE) formalism for solving RTEs in piecewise homogeneous media. Specifically, we propose to discretize SIEs pertinent to the RTE using classical Galerkin methods that are accelerated using fast summation techniques. We expect the new solver to require far fewer computational resources than existing differential equation RTE solvers.