Displacement1 estimation is an essential step for ultrasound elastography and numerous techniques have been proposed to improve its quality using two frames of ultrasound RF data. This paper introduces a technique for calculating a displacement field from three frames of ultrasound RF data. To this end, we first introduce constraints on variations of the displacement field with time using mechanics of materials. These constraints are then used to generate a regularized cost function that incorporates amplitude similarity of three ultrasound images and displacement continuity. We optimize the cost function in an expectation maximization (EM) framework. Iteratively reweighted least squares (IRLS) is used to minimize the effect of outliers. We show that, compared to using two images, the new algorithm reduces the noise of the displacement estimation. The displacement field is used to generate strain images for quasi-static elastography. Phantom experiments and in-vivo patient trials of imaging liver tumors and monitoring thermal ablation therapy of liver cancer are presented for validation.