The aim of this paper is to introduce anew three-dimensional elastoviscoplastic model that combines both the Oldroyd viscoelastic model and the Herschel-Bulkley viscoplastic model with a power-law index n > 0. The present model is derived to satisfy the second law of thermodynamics. Various fluids of practical interest, such as liquid foams, droplet emulsions or blood, present such elastoviscoplastic behavior: at low stress, the material behaves as a viscoelastic solid. whereas at stresses above a yield stress, the material behaves as a fluid. When n = 1, a recently introduced elastoviscoplastic model proposed by the author is obtained. When 0 < n < 1, then the plasticity criteria becomes smooth, the elongational viscosity is always well defined and the shear viscosity shows a shear thinning behavior. This is a major improvement to the previous elasroviscoplastic model. Finally, when n > 1, the material exhibits the unusual shear thickening behavior. (C) 2009 Elsevier B.V. All rights reserved.