The physics of bulk wurtzite-structure III-nitride materials and of III-nitride heterostructures includes many phenomena that can be modulated by the application of stress. In particular, p-type material is expected to display a rich variety of piezo-resistive and piezo-optic effects that originate from the stress-induced modulation of lattice polarization charges, of valence band energies, and of bulk, surface, and interface defect states in the band gap. Here we focus on the expected effects of in-plane uniaxial on p-channel AlGaN/GaN heterostructures grown along the hexagonal axis on sapphire substrates. The valence band structure in the channel region is calculated self-consistently in the framework of a six-band Rashba-Sheka-Pikus (RSP) Hamiltonian. Stress-effects are included (in linear elastic theory) through deformation potentials and through the modulation of interfacial polarization charges associated with the piezoelectric nature of the constituent materials.