Buckypaper (BP) is a planar film that consists of random network of multiwall carbon nanotubes (MWCNTs) held together by weak van der Waals interactions at tube-tube junctions. Although individual carbon nanotubes (CNTs) possess remarkable electrical properties, the electrical resistance of pristine BP is usually too high for practical applications. However, the electrical resistivity of BP can be attenuated by applying modest compressive stresses. Herein, we report an analytical model for predicting the electrical resistivity of BP under defined level of compressive strain. The predictive piezoresistive model of BP was developed by formulating a direct relationship with the structural parameters, physical and electrical properties of CNTs. The basis of the piezoresistive model relied upon the geometrical probability approach in combination with classical Hertzian contact mechanics and constriction resistance techniques. A comparison has been made between the theoretical and experimental results of electrical resistivity of BPs with varying densities. A reasonably good quantitative agreement was obtained between the theory and experiments. The main source of error was caused by the uncertainty in the measurement of the initial BP thickness. Through theoretical modeling, the initial volume fraction of CNTs was found to be one of the key parameters that modulated the piezoresistive behavior of BP.