We present a novel mesoscale model that describes the tensile stress of silica-filled polydimethylsiloxane (PDMS) under elongation. The model is based on atomistic simulations of a single chain of PDMS, interacting with itself and/or a hydroxylated silica surface. These simulations provide estimates of the microscopic forces required to stretch or uncoil a chain of PDMS, or detach it from a silica surface. For both stretching and detachment, we find that the internal potential energy is linear with the distance the chain end is moved, albeit with differing slopes. From these calculations and recent atomic force microscopy (AFM) experiments, we conclude that the forces are constant. We apply this analysis to the case of uncrosslinked, silica-filled PDMS systems and develop a mesoscale, inter-particle strength model. The strength model includes the atomistic forces determined from the simulations, a small entropic component, and a Gaussian probability distribution to describe the distribution of chain lengths of PDMS strands connecting two silica particles and the chain lengths in the free ends. We obtain an analytic stress/strain expression whose predictions agree with experiment. This model also suggests mechanisms to explain the phenomena of hysteresis and permanent set.