In this paper, we propose an energy-based joint motion-disparity estimation algorithm from the calibrated stereoscopic image sequences while preserving image discontinuities. We can estimate dense motion and disparity in the same method and compute initial dense disparity of the next frame using the constraint between motion and disparity in stereo image sequence. Using energy minimization approach, the field, which are motion and disparity, can be estimated in the same method and this method produces smooth field in object area while preserving its discontinuities of image boundaries. To preserve discontinuities and overcome a classic ill-posed problem, we use the regularization term proposed by Nagel-Enkelmann. We solve the Euler-Lagrange equation to minimize the energy functional and this partial differential equation is solved by the gradient descent method which is the most popular algorithm. And to avoid convergence to irrelevant local minima during iterations, we choose the proper initial data. Our experiment is performed on real stereoscopic sequences. Our experimental results showed that the proposed algorithm provides the accurate fields and the motion and disparity maps reflect the constraint of motion and disparity and preserve discontinuities of image boundaries well.