Flow of Bingham fluids in Couette-Poiseuille flow is studied. A set of analytically flow equations for flow between parallel plates/slots is presented, and used as a basis for developing simpler flow equations. A single flow equation explicit in the pressure gradient that approximates the full analytical solution for annulus is developed. For the special case when the diameter ratio approaches unity, we also present a simpler flow equation designed for slot flow. The new explicit flow equations are designed for application in dynamic ODE-based flow models, and may readily be combined with advanced pressure control and parameter estimation techniques. The performance of the new equation is shown to be good, and the concept presented here may be extended to the more general Herschel-Bulkley model. (C) 2012 Elsevier B.V. All rights reserved.