Gallium nitride (GaN) nanowires (NWs) have been intensely researched as building blocks for nanoscale electronic and photonic device applications; however, the mechanical properties of GaN nanostructures have not been explored in detail. The rigidity, thermal stability, and piezoelectric properties of GaN make it an interesting candidate for nano-electromechanical systems. We have fabricated doubly clamped GaN NW electromechanical resonators on sapphire using electron beam lithography and estimated the Young's modulus of GaN from resonance frequency measurements. For wires of triangular cross section with side ∼90 nm, we obtained values for the Young's modulus to be about 218 and 691 GPa, which are of the same order of magnitude as the values reported for bulk GaN. We also discuss the role of residual strain in the nanowire on the resonant frequency and the orientation dependence of the Young's modulus in wurtzite crystals.