Ultrasound elasticity imaging aims to reconstruct the distribution of elastic modulus (e.g., Young's modulus) within biological tissues, since the value of elastic modulus is often related to pathological changes. Currently, most elasticity imaging algorithms face a challenge of choosing the value of the regularization constant. We propose a more applicable algorithm without the need of any regularization. This algorithm is not only simple to use, but has a relatively high accuracy. Our method comprises of a nonrigid registration technique and tissue incompressibility assumption to estimate the two-dimensional (2D) displacement field, and finite element method (FEM) to reconstruct the Young's modulus distribution. Simulation and phantom experiments are performed to evaluate the algorithm. Simulation and phantom results showed that the proposed algorithm can reconstruct the Young's modulus with an accuracy of 63∼85%.