In several practical cases the material's elastic behaviour is very well described by Hooke's law. However, in alloys that exhibit a low Young's modulus and at the same time a high yield strength, such as the high-temperature near-alpha Titanium alloy Ti 6242S this is not the case. Ti 6242S is utilized mainly in the high-pressure compressor of jet engines. In such an environment the material undergoes fatigue loads. It is therefore necessary to ascertain the cyclic properties of the material at service temperature in order to guarantee safe life of the components. During low cycle fatigue tests at elevated temperatures (350; 450; 550 and 650°C) the elastic part of the deformation was calculated. The shape of the stress vs. strain response was not linear, as might have been expected, but rather crescent-like. This observation may be attributed to the fact that the elastic modulus is stress-dependent as a consequence of non-linear effects. This dependence was determined quantitatively. In order to establish the usual linearity of the elastic behaviour, Hooke's law was expanded by a quadratic term. In such a way it is characterized by two constants. While the Young's modulus remains a function of temperature, the second constant, named “K”, neither alters its value with temperature nor applied stress or strain amplitude. For Ti 6242S the value of K was calculated to be 210,000 MPa.