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[Display omitted] • We achieved epitaxial linear-piezoelectric ZnO films on flexible substrates. • We enhanced the linear-piezoelectric constant of ZnO with epitaxial strains. • We proved the trivial impacts of textures on the piezoelectric constant of ZnO. Ferroelectrics are popular for sensors, actuators and transducers. However, the energy barrier for reversing the polarization leads to extra energy losses, while the hysteresis causes phase-lags and non-linearities between input and output signals. The high piezoelectric constants of ferroelectrics dictate the figure-of-merit of piezoelectric devices. Enhancing the piezoelectric constant of linear-piezoelectrics potentially leads to next-generation piezoelectric devices free from issues associated with ferroelectrics. By epitaxial growth of undoped ZnO films on flexible Hastelloy substrates, we demonstrated an ~85% improvement in the piezoelectric constant, and more importantly maintained the linearity of the piezoelectric response. Strong out-of-plane and in-plane crystallographic alignments are detected in the epitaxial sample, yet modeling of the effective thin-film piezoelectric constant shows only a limited contribution of the optimized textures. The improvement in the piezoelectric response is ascribed mostly to the in-plane epitaxial strain resulted from the lattice mismatch of ZnO to the substrate. The epitaxial ZnO film on Hastelloy promisingly offer high-precision positioners with nano-/pico-meter resolutions. Enhancing the piezoelectric constant by strain engineering potentially removes the barrier for applications of linear-piezoelectrics and enriches the piezoelectric research community. [ABSTRACT FROM AUTHOR]