This work is an investigation into the curvature related potential for flux to flow in the radial direction in the back-iron of laminated axial flux machine cores. Analytical and numerical models are presented. Analysis based on these models has shown that, in practical axial flux machines, the radial component of the flux density can be neglected with respect to the flux density distribution in the core back-iron. It has also been found that if the core permeability, core conductivity and number of poles are sufficiently high then power loss due to curvature related cross-lamination flux is negligible compared to normal eddy current losses. A closed form expression to predict losses due to curvature related radial flux is also presented. This expression allows axial flux machine designers to make quick assessment of the need to consider these losses when designing axial flux machines.