Rheological quantification is important in many industries, the concrete industry in particular, e.g., pumping, form filling, etc. Instead of performing expensive and time-consuming experiments, numerical simulations are a powerful means in view of rheological assessment. However, due to the unclear numerical reliability and the uncertainty of rheological input data, it is important for the construction industry to assess the numerical outcome. To reduce the numerical domain of cementitious suspensions, we assessed the numerical finite volume simulations of Bingham paste pumping flows in OpenFOAM. We analysed the numerical reliability, first, irrespective of its rheological input by comparison with the literature and theory, and second, dependent on a certain rheological quantification by comparison with pumping experiments. Irrespective of the rheological input, the numerical results were significantly accurate. Dependent on the rheological input, a numerical mismatch, however, existed. Errors below 1% can be expected for proposed numerical rules of thumb: a bi-viscous regularisation, with pressure numbers higher than 5/4. To improve bias due to uncertain rheology, a rheological configuration close to the engineer’s aimed application should be used. However, important phenomena should not be overlooked. Further assessment for lubrication flows, in, e.g., concrete pumping, is still necessary to address concerns of reliability and stability.