Aiming at the potential high-temperature packaging material of the wide band gap semiconductors, experimental and theoretical analysis on the compressive properties of sintered nano-silver was performed. The viscoplastic properties of sintered nano-silver were investigated by compressive experiments with five loading rates, and the effects of loading rate on the ultimate strength and elastic modulus of sintered nano-silver were analyzed. According to the microstructure characteristics of sintered nano-silver, the damage framework including void volume fraction was developed by extending the Gurson–Tvergaard–Needleman model, and the mathematical model between Bonora damage law and void volume fraction was proposed, in which the internal void was assumed to be sphere and cube. A modified constitutive model including the damage model was developed based on the unified creep and plasticity theory for describing the compressive properties of sintered nano-silver. The accuracy of the proposed model was verified by comparing it with the experimental data.