Pinching is a degrading phenomenon which occurs during cyclic loading of certain materials. A change in the slope of the deflection curve reveals pinching lesions, either flexural cracks or bond degradation, cause pinching. This paper investigates pinching for 20 longitudinal and 18 alternate fully calcified osteonic samples of cylindrical shape and 500 micron length. Each sample was axially loaded beyond the proportional limit using an electromechanical device acting as a transducer of the variations in length of the sample into changes in the resonance frequency of a microwave micrometer. A cubic polynomial served as a mathematical model to investigate the stress-strain diagrams at the first and last cycles through the study of strain limits, stiffness and pinching behaviours, and energy absorption. The hysteretic behaviour of the two types of osteons differs and is far from ideal. The presence of pinching may derive from the existence of longitudinal fibrils, in particular the yielding of the incompletely calcified ones. In longitudinal osteons consisting mainly of longitudinal collagen fibrils, the deformation under compression is not protected by lamellae consisting of transverse fibrils, therefore the lesions inducing pinching are magnified. In contrast, in alternate osteons, where the fibrils having a longitudinal orientation are reduced and protected by lamellae containing transversely oriented fibrils, the lesions-inducing pinching are lessened.