We present an approximate numerical solution for the multiple scattering problem involving densely packed arbitrarily shaped small particles. We define incoherent volume elements that describe the statistics of the random medium and formulate an order-of-scattering solution for the entire random medium. We apply the T-matrix formalism to compute the incoherent interactions of irregular particles in the sequence of scattering events in the Monte Carlo radiative transfer algorithm. The T-matrices for the volume elements of arbitrarily shaped particles are computed by the volume-integral-equation (VIE)-based T-matrix method. We show that the approximate solution is in agreement with the numerically exact VIE solution for a small spherical random medium. Finally, we demonstrate the importance of applying irregular particle shape models in the analysis of multiple scattering by a large random medium of non-spherical particles.