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Purpose: MR‐Linac integrates an MRI scanner and a linear accelerator to provide adaptive radiation treatment. Superior tissue contrast and real‐time imaging can give the clinicians confidence to reduce the margins of the planning target volume (PTV). The purpose of this study was to verify the dosimetric accuracy of an MR‐Linac system in treating a moving target and assess the error with different motion patterns and adaptation methods. Methods: We performed an end‐to‐end test for Elekta Unity (Elekta) using the 4D Dynamic Thorax Phantom (CIRS MRgRT 008Z), comparing the measured and planned dose. The moving phantom had four measurement locations in the tumor, liver, kidney, and spinal cord regions with a PTW30013 ion chamber. For seven different motion patterns, we first acquired simulation CT using a slow‐scanning protocol, based on which we generated reference plans. The treatment technique was the standard intensity‐modulated radiation therapy (IMRT). We tested both adaptation workflows: the Adapt‐to‐Position (ATP) and the Adapt‐to‐Shape (ATS). The three‐dimensional (3D) distribution was measured using a diode array phantom (Sun Nuclear Inc.) to check the dose distribution accuracy as part of the routine QA process. We also performed end‐to‐end tests on a conventional Linac. Finally, we used SPSS Statistics 22.0 (Inc., Chicago, IL, USA) for data analysis. Results: All pretreatment reference plans and delivered plans had excellent QA results with a better than 95% passing rate of relative gamma analysis (2%/2 mm criteria). The adaptive planning for MR‐Linac produced quality plans. The measured dose in the target agreed with the calculated dose. Conclusions: The adaptive treatment on the MR‐Linac system investigated met the expected performance with tumor motions. The outline of the target could be visualized and accurately contoured on the 3D MR for online planning. Under different motion patterns, the difference between the measured and calculated dose was acceptable clinically. [ABSTRACT FROM AUTHOR]