Mechanical strain can modify the structural and electronic properties of methylammonium lead iodide MAPbI3. The consequences of ferroelastic hysteresis, which involves the retention of structural memory upon cycles of deformation, are reported for polycrystalline thin films of MAPbI3. Repeatedly bent films were examined using Grazing Incidence Wide-Angle X-ray Scattering (GIWAXS) to quantitatively characterize the strains and proportions of twin domains.Approximate locations for the coercive stress and saturation on the ferroelastic stress-strain curve are identified, and changes to the stress-strain curve with cyclic strain are characterized. Notably, an external stress source, such as thermal stress from the substrate or a roll-to-roll printing setup, must apply at least |50| MPa to modify the proportions of different twins. The presence of specific twin domains is found to correlate to previously-reported strain and defect heterogeneity in MAPbI3 films. Domains from differently-strained twin sets interact with each other. Long-term stability testing reveals that domain walls are highly immobile over extended periods. Nucleation of new domain walls occurs for specific mechanical strains and correlates closely with degradation. These results help to explain the behavior of ion migration, degradation rate, and photoluminescence in thin films under compressive and tensile strain.