We present experimental results on the dependence of the electrical conductivity of Mg-doped, p-type GaN on hydrostatic pressure and uniaxial stress. The samples were grown by molecular beam epitaxy on sapphire substrates. Hydrostatic pressure over the range studied (0-7 kbar) leads to a relatively small decrease in the conductivity. Uniaxial stress in the basal plane results in strongly increasing conductivity parallel to the stress direction and in weakly decreasing conductivity perpendicular to the stress direction. We relate the observed symmetry of the piezoconductivity to deformation potential induced changes in the band structure near the top of the valence band.