Many results from cyclic triaxial experiments indicate that porous media, such as clays, exhibit various long-term behaviours under different cyclic stress ratios (CSRs). These can be classified into three main categories, namely, cyclic shakedown, cyclic stable and cyclic failure. Modelling these soil deformation responses, along with pore pressure and other fundamental cyclic aspects, such as closed hysteresis cycles and degradation, is still an open challenge, and research to date is limited. In order to properly describe and capture these characteristics, an enhanced plasticity model, based on the bounding surface and stress distance concepts, is developed here. In detail, a new uniform interpolation function of the plastic modulus, suitable for all loading stages, is proposed, and a new damage factor associated with the plastic shear strain and the deformation type parameter, is also incorporated into the plastic modulus. Accordingly, cyclic shakedown and cyclic failure can be distinguished, and degradation is achieved. Closed hysteresis loops, typical of clays, are obtained through a radial mapping rule along with a moving projection centre, located by the stress reversal points. Comparisons between the obtained numerical results and the experimental ones from literature confirm the suitability of the constitutive approach, which is capable of correctly capturing and reproducing the key aspects of clays’ cyclic behaviour.