High rates of degradation in corrosive media represent the Achilles heel of Mg alloys, which hinders their applications in various areas, particularly in prosthetics. We present an investigation of the degradation behaviour of magnesium alloy AZ31 in Hank's solution that simulates bodily fluids. The degradation rate is shown to be significantly reduced by grain refinement produced by mechanical processing. In particular, hot rolling does lead to a desirable retardation of degradation, while subsequent equal channel angular pressing does not result in any further reduction of degradation rate.