Exploiting an electrostatic analogy, we show that the elastic forces between a set of rigid particles embedded in a phantom polymer network can be represented by a simple bead-and-spring model. The beads represent the particles and the springs the rubber matrix. The model is validated by Monte Carlo simulation of rubbers filled with hard spherical particles, at volume fractions between 0.1 and 0.3. We derive both the moduli and the full stress-strain curves, under uniaxial elongation. The model reproduces and extends previous theoretical results on the so-called hydrodynamic reinforcement effect.