Fundamental physical properties of wheat endosperm were characterized in soft and hard common wheats (T. aestivum), and durum wheats (T. durum), and studied in relation to NIR hardness. A positive correlation was observed between NIR hardness and compressive strength (Smax), energy to failure (Wmax), strain to failure (emax), and the tangent modulus of elasticity (E). The Smax values increased asymptotically with increasing NIR hardness. Energy to failure (Wmax), and strain to failure (e.max) increased with increasing NIR hardness, especially in the range of the durum wheats. The tangent modulus of elasticity (E) generally increased with rising NIR hardness values, except for the durum wheats, which fell within the upper range of the hard wheats. Wheat hardness appeared related to differences in both the strength and ductile properties of the endosperm. The compressive strength of wheat endosperm was affected by moisture content, deformation rate, and the direction of the stress forces. Values for (Smax), decreased as the moisture content of the endosperm increased. The decrease was greatest for hard wheats. Varietal differences in values for (Smax), were not significant at moisture levels of 22 % or higher. An increase in deformation rate from 0·5 mm/min to 500 mm/min increased Smax values by 34%. Endosperm strength was 10-fold greater under compression than under tension. © 1991, Academic Press Limited. All rights reserved.