Understanding a partial discharge mechanism at direct current (DC) is an actual research topic that requires both modeling, simulations and measurements. This paper describes an influence of insulating material properties on partial discharges at DC voltage. Modifications of the traditional model reflecting the conditions of partial discharges (PD) inception and post discharge processes at DC voltage have been proposed. The aim was to show the partial discharge mechanisms and draw attention to the role of parameters of insulation materials adjacent to the cavity at DC voltage. The investigations were performed on two kinds of dielectric material used in power cables. Various combinations of specimens were designed to reveal the effect of the material resistivity on the PD activity. Key observations referred to the impact of the void adjacent material resistance on the partial discharge inception voltage threshold at DC voltage. The modified PD model was applied to analyze both inception and post discharge recovery stage. The role of dielectric properties of material adjacent to the void was investigated, highlighting its impact during static inception stage and in charging stage. Despite many simplifications introduced in the model, measurement results have confirmed the role of the dielectric material surrounding the void on partial discharge dynamics. The average time interval between PD pulses revealed a systematic relationship with respect to the applied voltage and specimen resistivity. This value can be considered in the future research for diagnostic indicator at DC voltage.