We performed torsion tests of cork cylinders with a superimposed axial compression (biaxial tests). The axis of the cylindrical samples was, in different tests, along the radial or tangential direction in cork (respectively parallel and perpendicular to the rows of prismatic cells). We obtained the corresponding shear moduli and studied the effect of the superimposed axial compression. We also studied the effect of the rate of torsion on the shear moduli.