The mechanical behaviour of natural geomaterials is often anisotropic. Sedimentary rocks usually show a limited form of anisotropy, called cross-anisotropy. This paper presents an original constitutive model based on a hardening Drucker-Prager elasto-plastic framework that has been adapted to consider cross-anisotropic elasticity as well as an anisotropic plastic criterion. The cohesion is a function of the angle between the direction of the major compressive stress and the normal to the bedding plane. This original model consists in a relatively simple upgrading of a well-known elasto-plastic model, well-adapted for sedimentary hard soils or soft rocks. The ability of the model to reproduce the directional dependency of the elasto-plastic response of clay rocks, as observed in triaxial tests, is proved by numerical simulations of experimental tests.