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3D human motion capture from monocular RGB images respecting interactions of a subject with complex and possibly deformable environments is a very challenging, ill-posed and under-explored problem. Existing methods address it only weakly and do not model possible surface deformations often occurring when humans interact with scene surfaces. In contrast, this paper proposes MoCapDeform, i.e., a new framework for monocular 3D human motion capture that is the first to explicitly model non-rigid deformations of a 3D scene for improved 3D human pose estimation and deformable environment reconstruction. MoCapDeform accepts a monocular RGB video and a 3D scene mesh aligned in the camera space. It first localises a subject in the input monocular video along with dense contact labels using a new raycasting based strategy. Next, our human-environment interaction constraints are leveraged to jointly optimise global 3D human poses and non-rigid surface deformations. MoCapDeform achieves superior accuracy than competing methods on several datasets, including our newly recorded one with deforming background scenes.