Thixotropy is a reversible time-dependent phenomenon in fluids, in which an internal structure grows due to flocculation and breaks down under shear action. Numerous fluids are thixotropic, e.g. concretes and cementitious suspensions. Pumping of concrete is an important application. Since current approaches omit thixotropic effects, we aim to develop a simple theoretical model to evaluate or understand the significance of thixotropy on the concrete pumping behaviour. We therefore extended Poiseuille flow for thixotropic concretes and reformulated it in a dimensionless form to gain insights. After a validation, the results and significance are elaborated and concluded. Results showed that for increasing thixotropy and decreasing flow rates, the plug radius, wall shear rate and pumping pressure loss increase. Even though all thixotropy mechanisms may not be covered, a simple model is delivered to interpret or predict the effect of thixotropy on the pumping behaviour of cementitious suspensions. The dimensionless formulations via the Bingham number Bn and related discharge diagrams are sufficiently elegant for computational implementation and very insightful to distinguish a thixotropic flow regime. The model could be extended for more complicated thixotropies, irreversible time-dependent effects or even other pumping related phenomena.