We investigate the multiple scattering of waves by dense random distribution of particles. Maxwell equations are put in the form of Foldy-Lax multiple-scattering equations which are solved numerically. The positions of the particles are generated by random shuffling and bonding. Simulations are performed for applications in microwave scattering by terrestrial snow. The results are illustrated for the copolarization and cross-polarization scattering phase matrices and the extinction coefficients for sticky particles. We consider concentrations of particles up to 40% by volume. Results of dense media simulations depart from the predictions on the basis of classical theory of independent scattering and are applicable for very low concentrations. The simulation results agree with those of quasi-crystalline approximation (QCA) for concentration up to 20%. However, they start to deviate from those of the QCA for higher concentrations as QCA underestimates the extinction. Simulation results also predict strong cross polarization in the phase matrix of densely packed spheres, a result that is not predicted by classical independent scattering nor by QCA.