A novel and rational approach based on Lie analysis is proposed to investigate the mechanical behaviour of materials exhibiting experimental master curves. Our approach relies on the idea that the mechanical response of materials is associated with hidden symmetries; the general objective of this contribution is to reveal those symmetries from measurements and to construct constitutive laws from them. This approach provides a priori two ways of formulating constitutive laws from data as well as the possibility of predicting new master curves and material charts. The first part of the paper is devoted to the presentation of the general methodology. Afterwards, the strategy is applied to the uniaxial creep and rupture behaviour of a Chrome-Molybdene alloy (9Cr1Mo) at different temperatures and stress levels. Constitutive equations for creep and rupture master responses are identified for this alloy and validated on experimental data.