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 (LAOS). 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.