From a thermodynamic theory, a new model for elastoviscoplastic fluid flow is presented. It extends the Bingham viscoplastic model and the Oldroyd viscoelastic model. Fundamental flows are studied: simple shear flow, uniaxial elongation and large amplitude oscillatory shear. The complex moduli (G',G'') are founded to be in qualitative agreement with experimental data for materials that present microscopic network structures and large scale rearrangements. 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.