We have developed a quantum anisotropic transport model for holes which, for the first time, allows mobility to be studied under both uniaxial and arbitrary stress in PMOS inversion layers. The anisotropic bandstructure of a 2D quantum gas is computed from a 6-band stress dependent k.p Hamiltonian. Our unique momentum-dependent scattering model also captures the anisotropy of scattering. A comprehensive study has been performed for uniaxial stress, biaxial stress, and their nonlinear interactions. The results are compared with device bending data and piezoresistance data, showing very good agreement.