The triaxial creep experiments of a kind of claystone was performed with a specially designed triaxial creep testing device; and the effects of axial stress σ1 and confining pressure σ3 on the creep are investigated. It was found that for constant confining pressure, creep develops faster, the steady-state creep strain rate increases, and the life is reduced, with the increase of axial stress. If the stress difference ?σ =σ1–σ3 is constant, creep strain and steady-state creep strain rate decrease and the life increases with the increase of confining pressure. The creep behavior of claystone was analyzed with an elastic-viscoplastic constitutive model for incorporating damage and its evolution. It is shown that the main features observed in experiments can be satisfactorily described.