The structure and energies of the cores of  and  screw dislocations in wadsleyite (β-Mg2SiO4) are calculated using a cluster-based combined elastic-atomistic method and a new parameterized interatomic potential model. For a core radius of 10 Å, core energies are found to be 2.5 and 4.4 eV/Å for the  and  dislocations, respectively. Both dislocations are associated with significant non-elastic displacement fields extending beyond the core with a radial component toward the dislocation line. The core of the  dislocation contains tetrahedrally coordinated magnesium, has a simple 2D structure and is spread parallel to (011) in a manner that suggests high mobility. In contrast, the core of the  dislocation has an extended and complex 3D structure involving the formation a large Si6O19 unit twisted around the dislocation line. This implies that movement of the  dislocation will be inhibited by the need to cleave Si–O bonds. These observations, combined with the anomalously low core energy of the  dislocation, explain the regular occurrence of  dislocations and very rare observation of  dislocations in experimentally deformed wadsleyite samples.