We report the hardness of wurtzite InN thin film grown with different crystalline orientations of heteroepitaxial s-plane (1101) and a-plane (1120) on r-plane (1102) Al2O3, and homoepitaxial film on c-plane (0001) Al2O3. Hardness values along with elastic properties are studied using nanoindentation technique. Maximum hardness is reported for c-plane (approximately 8 GPa), which is followed by s-plane (approximately 5.5 GPa) and then a-plane (approximately 4 GPa) oriented InN Films. Peierls force in the slip system of different crystalline orientations for wurtzite sample is calculated for explaining the systematic variations in hardness values of these films grown with different crystalline orientations.