The paper proposes two new elastoplastic constitutive models for the description of deformation mechanisms of frictional materials which are suitable for a wide range of applications in soil mechanics. The first model provides an extension of the classical Drucker-Prager-type function in order to overcome numerical difficulties in the tensile stress range. The key idea here is the introduction of a constant perturbation-type parameter which yields a C-2-differentiable smoothing-out of the peak of the Drucker-Prager cone. We then extend this formulation to a closed single-surface model based on a decoupled description of the deviatoric and the mean stress response. Both models are equipped with a saturation-type hardening mechanism. They have proved to be very robust and successful in numerical implementations.