We develop an analytic model for the lensing mass of galaxies, based on a broken power-law (BPL) density profile, which is a power-law profile with a mass deficit or surplus in the central region. Under the assumption of an elliptically symmetric surface mass distribution, the deflection angle and magnification can be evaluated analytically for this new model. We compute the theoretical prediction of various quantities, including the volume and surface mass density profiles of the galaxies, and the aperture and luminosity (AL)-weighted line-of-sight velocity dispersions (LOSVDs), and compare to those measured from the Illustris simulation. We find an excellent agreement between our model prediction and the simulation, which validates our modeling. The high efficiency and accuracy of our model manifests itself a promising tool for studying properties of galaxies with strong lensing.