Computational stereo is in the fields of computer vision and photogrammetry. In the computational stereo and surface reconstruction paradigms, it is very important to achieve appropriate epipolar constraints during the camera-modeling step of the stereo image processing. It has been shown that the epipolar geometry of linear pushbroom imagery has a hyperbola-like shape because of the non-coplanarity of the line of sight vectors. Several studies have been conducted to generate resampled epipolar image pairs from linear pushbroom satellites images; however, the currently prevailing methods are limited by their pixel scales, skewed axis angles, or disproportionality between x-parallax disparities and height. In this paper, a practical and unified piecewise epipolar resampling method is proposed to generate stereo image pairs with zero y-parallax, a square pixel scale, and proportionality between x-parallax disparity and height. Furthermore, four criteria are suggested for performance evaluations of the prevailing methods, and experimental results of the method are presented based on the suggested criteria. The proposed method is shown to be equal to or an improvement upon the prevailing methods.