The influence of biaxial stress on the maximum and remanent polarizations of 10 nm thick hafnium zirconium oxide thin films in metal–ferroelectric–metal capacitor structures has been quantified. In the as-prepared state with a nominal biaxial tensile strain of 0.20% and no applied extrinsic stress, remanent and maximum polarizations of 7.6 and 13.1 μC/cm2, respectively, were measured using a 2 MV/cm applied electric field. Reducing the intrinsic strain by 0.111% through the application of a compressive uniaxial stress results in a decrease in the remanent and maximum polarizations to 6.8 and 12.2 μC/cm2, respectively. The polarization dependence on strain is nearly linear between these values. The observed variation in polarization with strain is consistent with strain impacting ferroelastic switching whereby in-plane tension increases the fraction of the short polar axis orienting out-of-plane, hence increasing out-of-plane polarization. In contrast, reducing the in-plane strain through compression results in an increase in the fraction of the long non-polar axis orienting out-of-plane, thereby decreasing out-of-plane polarization.