The magnesium alloy AZ31 was processed by severe hot rolling and annealing. This processing was optimised to produce recrystallised grain sizes as small as 2.2 μm. The texture of the processed plate was similar to that of the as-received material, with a strong basal alignment in the normal direction. Tensile testing of the fine grained material showed an increase in the strength and elongation compared to the as-received plate. It is concluded that the improved mechanical properties of the fine grained material results from a refinement in the grain size and the elimination of shear bands that pre-exist in the as-received material.