This paper presents a new three-dimensional elastic viscoplastic (3D EVP) constitutive model for the time-dependent stress-strain behaviour of both normally consolidated and overconsolidated clays. There are two major new developments in the 3D EVP model: (i) incorporation of a nonlinear creep function with a limit for the creep volume strain under isotropic stressing conditions; (ii) adoption of a new loading surface function with a smooth shape on the pie plane. Based on the "equivalent time" concept of Yin and Graham, the formulation of the new 3D EVP model is derived using the new nonlinear creep function and loading surface function. A new approach to determining all model parameters is presented. The 3D EVP model is calibrated using data from one conventional isotropic stress creep test and consolidated-undrained triaxial tests on soft Hong Kong marine deposits (HKMD). The model is verified by comparing model results with those from both normally and overconsolidated triaxial tests on HKMD and a mixture of kaolin and bentonite.