In high-power pulsed laser ablation of metals, the material removal usually occurs in the regime of volumetric boiling, when the ablated materials form two-phase plasma plumes composed of neutral atoms, ions, electrons, and a large fraction of nanoparticles/clusters. To predict the effect of plasma shielding induced by absorption of laser radiation in such twophase plumes, a hybrid multi-phase computational model is developed. The model includes a thermal model of the irradiated target, a model of non-equilibrium ionization of gaseous plasma plume based on the collision-radiation plasma model, and a kinetic equation that describes the distribution of cluster sizes and temperatures. The model accounts for the fragmentation of the target material in the regime of volumetric boiling, evaporation and condensation of nanoparticles, as well as radiation absorption and scattering by all constituents of the plume. The model is used to evaluate the contributions of various factors on the degree of plasma shielding at laser ablation of a copper target irradiated by a nanosecond laser pulse. The simulations show that the radiation scattering by nanoparticles is the dominant mechanism of radiation attenuation. The cluster evaporation and attenuation of laser radiation by nanoparticles are found to have a strong effect on plume dynamics and plasma shielding.