The passive and active properties of the cochlear outer hair cell are studied. The outer hair cell is currently considered the major candidate for the active component of mammalian hearing. Understanding of its properties may explain the amplification and sharp frequency selectivity of the ear. To analyse the cell behaviour, a model of a nonlinear anisotropic electro-elastic shell is used. Using the data from three independent experiments, where the mechanical strains of the cell are measured, estimates of the cell wall in-plane Young's moduli and Poisson's ratios are given, as well as estimates of three modes of bending stiffness. Based on these estimates and data from the microchamber experiment, where the cell is under the action of transmembrane potential changes, the characteristics of the outer hair cell active behaviour are found. These characteristics include the coefficients of the active force production per unit of the transmembrane potential change and limiting parameters of the electromotile response for extreme hyperpolarisation and depolarisation of the cell. The obtained estimates provide important information for the modelling of organ-level cochlear mechanics.