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The influence of carbon at dislocation cores in α-Fe is studied to determine the Peierls stress, i.e. the critical stress required to move the dislocation at 0 K. The effect of carbon on both edge and screw dislocations is investigated. A coupled molecular statics (MS) and extended finite element method (XFEM) is employed for this study, where the dislocation core is modeled atomistically. The results on pure Fe are found to be in good agreement with a fully atomistic study. The coupled approach captures the right core behavior and significantly reduces the size of the atomistic region, while describing the behavior of a single dislocation in an infinite anisotropic elastic medium. Furthermore, mechanical boundary conditions can be applied consistently. It was found that the influence of carbon on edge dislocations is much stronger than that on screw dislocations, and that carbon causes a directionally dependent Peierls stress in the case of a screw dislocation. Even though the increase of the Peierls stress is much more pronounced for edge dislocations, the total value does not reach the level of the Peierls stress for screw dislocations, either with or without carbon at the core. Hence, we conclude that the motion of screw dislocations remains the rate limiting factor for plastic deformation of The influence of carbon at dislocation cores in α-Fe is studied to determine the Peierls stress, i.e. the critical stress required to move the dislocation at 0 K. The effect of carbon on both edge and screw dislocations is investigated. A coupled molecular statics (MS) and extended finite element method (XFEM) is employed for this study, where the dislocation core is modeled atomistically. The results on pure Fe are found to be in good agreement with a fully atomistic study. The coupled approach captures the right core behavior and significantly reduces the size of the atomistic region, while describing the behavior of a single dislocation in an infinite anisotropic elastic medium. Furthermore, mechanical boundary conditions can be applied consistently. It was found that the influence of carbon on edge dislocations is much stronger than that on screw dislocations, and that carbon causes a directionally dependent Peierls stress in the case of a screw dislocation. Even though the increase of the Peierls stress is much more pronounced for edge dislocations, the total value does not reach the level of the Peierls stress for screw dislocations, either with or without carbon at the core. Hence, we conclude that the motion of screw dislocations remains the rate limiting factor for plastic deformation of α-Fe.