Young’s modulus and Poisson’s ratio are related to quantitative reservoir properties such as porosity, rock strength, mineral and total organic carbon content, and they can be used to infer preferential drilling locations or sweet spots. Conventionally, they are computed and estimated with a rock physics law in terms of P-wave, S-wave impedances/velocities, and density which may be directly inverted with prestack seismic data. However, the density term imbedded in Young’s modulus is difficult to estimate because it is less sensitive to seismic-amplitude variations, and the indirect way can create more uncertainty for the estimation of Young’s modulus and Poisson’s ratio. This study combines the elastic impedance equation in terms of Young’s modulus and Poisson’s ratio and elastic impedance variation with incident angle inversion to produce a stable and direct way to estimate the Young’s modulus and Poisson’s ratio, with no need for density information from prestack seismic data. We initially derive a novel elastic impedance equation in terms of Young’s modulus and Poisson’s ratio. And then, to enhance the estimation stability, we develop the elastic impedance varying with incident angle inversion with damping singular value decomposition (EVA-DSVD) method to estimate the Young’s modulus and Poisson’s ratio. This method is implemented in a two-step inversion: Elastic impedance inversion and parameter estimation. The introduction of a model constraint and DSVD algorithm in parameter estimation renders the EVA-DSVD inversion more stable. Tests on synthetic data show that the Young’s modulus and Poisson’s ratio are still estimated reasonable with moderate noise. A test on a real data set shows that the estimated results are in good agreement with the results of well interpretation.