We study the electromagnetic wave propagation in three-dimensional (3-D) dense random discrete media containing dielectric spheroidal scatterers. We employ a Monte Carlo method in conjunction with the Method of Moments to solve the volume integral equation for the electric field. We calculate the effective permittivity of the random medium through a coherent-field approach and compare our results with a classical mixing formula. A parametric study on the dependence of the effective permittivity on particle elongation and fractional volume is included.