The structure and residual stresses of ZnO films synthesized by a planar magnetron sputtering system with two facing targets were investigated by X-ray diffraction. ZnO films were deposited onto a sheet of Coming 7059 glass. The X-ray diffraction pattern shows that the film has high {00.1} orientation. Residual strains were measured on various diffraction lines that appear at special angles psi from the surface normal. The strains taken from positive and negative psi differed from each other. This behavior is deduced from the existence of a shear stress component in a cross-section of the film. The magnitude of the shear stress increased with increasing current density of the Zn target as well as with decreasing argon gas pressure.