Yttria Stabilised Zirconia (YSZ) is a tough, phase-transforming ceramic that finds use in a wide range of commercial applications from dental prostheses to thermal barrier coatings. Micromechanical modelling of phase transformation can deliver reliable predictions in terms of the influence of temperature and stress. However, models must rely on the accurate knowledge of single crystal elastic stiffness constants. Some techniques for elastic stiffness determination are well-established. The most popular of these involve exploiting frequency shifts and phase velocities of acoustic waves. However, the application of these techniques to YSZ can be problematic due to the micro-twinning observed in larger crystals. Here, we propose an alternative approach based on selective elastic strain sampling (e.g., by diffraction) of grain ensembles sharing certain orientation, and the prediction of the same quantities by polycrystalline modelling, for example, the Reuss or Voigt average. The inverse problem arises consisting of adjusting the single crystal stiffness matrix to match the polycrystal predictions to observations. In the present model-matching study, we sought to determine the single crystal stiffness matrix of tetragonal YSZ using the results of time-of-flight neutron diffraction obtained from an in situ compression experiment and Finite Element modelling of the deformation of polycrystalline tetragonal YSZ. The best match between the model predictions and observations was obtained for the optimized stiffness values of C11 = 451, C33 = 302, C44 = 39, C66 = 82, C12 = 240, and C13 = 50 (units: GPa). Considering the significant amount of scatter in the published literature data, our result appears reasonably consistent.