Tubular specimens machined from extruded AZ31B were tested under cyclic axial and cyclic torsional loading conditions. Pure cyclic axial and pure cyclic torsional behaviour is characterised and presented from macroscopic and mechanistic viewpoints. Unlike the asymmetric hysteresis observed under cyclic axial loading, extruded AZ31B behaves symmetrically under cyclic torsional loading. It is shown that cyclic shear response can be successfully modelled by the Ramberg–Osgood cyclic relation and the corresponding parameters were obtained and presented. This material experiences a significant cyclic hardening and plastic strain reduction in cyclic axial loading. The cyclic shear hardening is less pronounced. Energy, as a scalar valued function independent of direction, is proposed as a potential fatigue parameter that can provide an equivalent damage measure in multiaxial loading for anisotropic materials. It is shown that the total energy densities, the sum of plastic and positive energy densities at half-life, correlate the fatigue data in both axial and torsional loading.