Technical Abstract: Endosperm texture is one of the most important quality features in wheat that defines milling energy requirements and the suitability of flour or semolina for the various food products such as pan breads, crackers, cakes, and pastas. Rooted in low molecular weight proteins known as puroindolines a and b through an inverse relation to adhesive strength of the starch-protein interface, texture is quantified by measuring the physical property of the resistance force to crushing of precisely machined specimens of endosperm. In such procedures, cylindrical or parallelepiped blocks are crushed under a constant rate of strain, in which values are reported of maximum stress, strain at maximum stress, Young’s modulus, and the energy of compression to the point of maximum stress. Generally overlooked, however, is the influence of the instrument itself which can significantly affect the values of three of these properties. Because no instrument is infinitely rigid, departures between apparent and actual strength properties occur. In this study, the physical principles for compressive strength measurement with respect to corrections for instrument rigidity are developed. It is shown that the departures are exacerbated in specimens of small slenderness (ratio of height to lateral dimension) and large hardness. This is demonstrated in a small collaborative study involving three laboratories and three instruments of low, intermediate, and high rigidity. Specimens were prepared from wheat kernels from hard and soft near-isogenic lines derived from the cultivar Alpowa. For strain at maximum stress, the implementation of a correction for instrument rigidity reduced the range across laboratories from 6.03-47.7% (before correction) to 4.49-7.35% (after correction) for the hard genotype, while the corresponding ranges for the soft genotype were 3.29-18.6% and 2.07-6.01%. For Young’s modulus, instrument rigidity correction resulted in a tenfold correction for the hard genotype measured on the least rigid instrument, going from 0.21 GPa (before) to 4.9 GPa (after). Likewise with this instrument, the imparted energy density to maximum stress was reduced from an average apparent value of 23 MJ/m^3 (before) to 3.8 MJ/m^3 (after). Because of these large differences between apparent and actual values for these physical strength properties, it is recommended that future strength property measurements should account for instrument rigidity by implementation of the correction procedure described herein.