An analytical model is proposed which relates the bonding temperature, pressure, and duration with the integrity of metal-metal thermocompression bonds. Unlike previous models, this approach takes into account the pressure-dependent time evolution of the thermocompression bond formation. The model allows calculation of the true contact area of rough surfaces, based on a creep-dominated plastic deformation. Verification of the model was provided through experiments on Cu-Cu thermocompression bonds of electroplated Cu on diced silicon wafers with chemical-mechanical polished surfaces. The samples were bonded at a range of temperatures, pressures, and times. Shear strength measurements were used to characterize the effects of the bonding parameters on the interface bond strength. Calculated true contact area and bond shear strength can be related by a single proportionality factor. The model can be used to predict the thermocompression bond quality for given bonding parameters and process optimization for reliable bonds, thus assisting in the adoption of the Cu thermocompression bond process in the three-dimensional integrated circuits applications.