There is currently intense interest in the properties of several of the III-V semi-conductors. Of these, gallium nitride (GaN) is currently attracting greatest interest. This is because of its large band-gap, which gives it potential for application in opto-electronic devices operating in the blue region of the spectrum. Due to its crystal structure, gallium nitride has spontaneous polarization and is piezoelectric. The piezoelectric field in strained GaN can have a significant effect on its properties in electronic devices and indeed the effect has been exploited in this area. We have used an interferometric technique to measure the field induced strain in thin GaN films, leading to values for the d33 piezoelectric coefficient. The measurements have been made both for sputtered polycrystalline films and for commercial wafers which have single crystal orientation. We have also found that the measured piezoelectric coefficient varies with an applied bias field. This suggests that GaN also possesses a significant electrostrictive response and a value for the electrostrictive coefficient M33 has been deduced from the data.