A simple extension of an incrementally nonlinear, so-called hypoplastic constitutive model, which was originally proposed for cohesionless sand, is presented with respect to cohesive powders, Motivated by the effect of capillary force, an internal state variable representing an intrinsic pressure is introduced. The model is then extended by adding the intrinsic pressure to the actual stress. The material parameters in the extended model can be identified with conventional experiments. Numerical simulations of several laboratory tests, including oedometer and triaxial tests, are presented. By comparing the predicted relation between tensile strength and consolidation pressure with experimental data on limestone powder available in the literature, it is shown that the extended model is capable of reproducing the salient behaviour of cohesive powders, e.g. the nonlinear stress-strain relation, dilatant volume change upon shearing and the dependence of the tensile strength on the consolidation pressure.