We present results of a theoretical study of the electronic band structure of wurtzite InN films under biaxial strain in the C-plane (0001) and in planes that correspond to non-polar orientations such as the A-plane (112̄0) and the M-plane (11̄00). The calculations are performed under the k · p perturbation theory approach using the Bir-Pikus Hamiltonian. The results show that the fundamental bandgap of InN shifts by 30 meV (14 meV) for isotropic tensile (compressive) strain in the C-plane with out-of-plane contraction (dilation) of 0.2%. For films of non-polar orientations, the c-axis lies in the film plane and the strain is expected to be different between directions parallel and perpendicular to c. Such anisotropic strain give rise to valence band mixing which results in dramatic changes in the optical polarization properties as evidenced by the calculated oscillator strengths of the interband transitions. © 2007 WILEY-VCH Verlag GmbH & Co. KGaA.