Purpose: To incorporate a newly developed shape-based motion estimation scheme into magnetic resonance urography (MRU) and verify its efficacy in facilitating quantitative functional analysis. Methods: The authors propose a motion compensation scheme in MRU that consists of three sequential modules: MRU image acquisition, motion compensation, and quantitative functional analysis. They designed two sets of complementary experiments to evaluate the performance of the proposed method. In the first experiment, dynamic contrast enhanced (DCE) MR images were acquired from three sedated subjects, from which clinically valid estimates were derived and served as the "ground truth." Physiologically sound motion was then simulated to synthesize image sequences influenced by respiratory motion. Quantitative assessment and comparison were performed on functional estimates of Patlak number, glomerular filtration rate, and Patlak differential renal function without and with motion compensation against the ground truth. In the second experiment, the authors acquired a temporal series of noncontrast MR images under free breathing from a healthy adult subject. The performance of the proposed method on compensating real motion was evaluated by comparing the standard deviation of the obtained temporal intensity curves before and after motion compensation. Results: On DCE-MR images with simulated motion, the generated relative enhancement curves exhibited large perturbations and the Patlak numbers of the left and right kidney were significantly underestimated up to 35% and 34%, respectively, compared with the ground truth. After motion compensation, the relative enhancement curves exhibited much less perturbations and Patlak estimation errors reduced within 3% and 4% for the left and right kidneys, respectively. On clinical free-breathing MR images, the temporal intensity curves exhibited significantly reduced variations after motion compensation, with standard deviation decreased from 30.3 and 38.2 to 8.3 and 11.7 within two manually selected regions of interest, respectively.