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The asymptotic fields near the tip of a stationary crack in a strain gradient elastic material under Mode III loading conditions are investigated by adopting the indeterminate theory of couple stress elasticity with two characteristic lengths. The adopted constitutive model is able to account for the underlying microstructure of the material as well as for the strong size effects arising at small scales. The effects of microstructure on Mode III crack tip fields mainly consist in a substantial increase in the singularities
of the skew-symmetric stress and couple stress fields thus resulting in a significant increase of the tractions level ahead of the crack-tip. Correspondingly, the symmetric stress field turns out to be nonsingular. These results agree with the findings of the asymptotic analysis performed for a single material characteristic length. However, the angular variations of the crack tip fields and the energy release rate turn out to be strongly influenced by the ratio between the two characteristic lengths.