In this study, the steady pipe flow of a thixo-elastic fluid is considered. Thixo-elasticity is modeled using the modified Delaware thixotropic model (MDTM). In MDTM model, the total stress tensor is decomposed into a viscous part and an elastic part and each stress component is properly modeled using the concept of single structural parameter which represent the state of thixotropic microstructure in space and time. Analytical solutions are attained for three special cases of MDTM model and a general semi-analytical solution is devised as well. The effect of various thixo-elastic parameters is studied on the profiles of axial velocity and structural parameter. Additionally, volumetric flow rate is presented for all the considered cases. (C) 2017 Elsevier B.V. All rights reserved.