The change in core structure of the screw dislocation in a body-centred cubic lattice subjected to a general applied stress tensor is studied by means of computer simulation. The large variations observed are found not to be correlated with the applied stress, in that the same deformed core structure can be realized by many different combinations of stress components. Instead, the core structure is found to be characterized almost exclusively by the magnitude and orientation of the induced glide strain, with a much smaller dependence on the glide stress. This means that while the force acting on a dislocation is defined by the applied stress, it is the elastic strain within the lattice that determines the resistance to motion. This explains the anomalously large dependence of the Peierls stress upon non-glide components of the applied stress tensor. The Peierls stress varies strongly with the shape of the dislocation core, which depends upon the glide strain. However, the glide strain is in turn dependent on non-glide components of the applied stress by way of anisotropic elastic couplings. Therefore the Peierls stress is itself dependent on the non-glide stresses, to an extent governed by the elastic anisotropy. The possible origin of the strain-dependence of the core structure in elastic strain multiplet forces (equal and opposite generalized forces acting on the dislocation) is discussed briefly, as are implications for the phenomenon of ductile fracture.