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Objective. The Elekta unity MR-linac delivers step-and-shoot intensity modulated radiotherapy plans using a multileaf collimator (MLC) based on the Agility MLC used on conventional Elekta linacs. Currently, details of the physical Unity MLC and the computational model within its treatment planning system (TPS) Monaco are lacking in published literature. Recently, a novel approach to characterize the physical properties of MLCs was introduced using dynamic synchronous and asynchronous sweeping gap (aSG) tests. Our objective was to develop a step-and-shoot version of the dynamic aSG test to characterize the Unity MLC and the computational MLC models in the Monaco and RayStation TPSs. Approach. Dynamic aSG were discretized into a step-and-shoot aSG by investigating the number of segments/sweep and the minimal number of monitor units (MU) per segment. The step-and-shoot aSG tests were compared to the dynamic aSG tests on a conventional linac at a source-to-detector distance of 143.5 cm, mimicking the Unity configuration. the step-and-shoot aSG tests were used to characterize the Unity MLC through measurements and dose calculations in both TPSs. Main results. The step-and-shoot aSGs tests with 100 segments and 5 MU/segment gave results very similar to the dynamic aSG experiments. The effective tongue-and-groove width of the Unity gradually increased up to 1.4 cm from the leaf tip end. The MLC models in RayStation and Monaco agreed with experimental data within 2.0% and 10%, respectively. The largest discrepancies in Monaco were found for aSG tests with >10 mm leaf interdigitation, which are non-typical for clinical plans. Significance. The step-and-shoot aSG tests accurately characterize the MLC in step-and-shoot delivery mode. The MLC model in RayStation 2023B accurately describes the tongue-and-groove and leaf tip effects whereas Monaco overestimates the tongue-and-groove shadowing further away from the leaf tip end. [ABSTRACT FROM AUTHOR]