Isothermal, steady-state and fully developed flows of Ellis fluids in plana and annular slits are discussed. The flow equations derived for Ellis fluids describe also the flows of Newtonian and power law fluids as specific cases. The most important flows resulting from the general theory, i.e., the pressure flows in flat and annular slits for stationary channel walls, and at transverse and longitudinal movements of a wall, are analyzed in detail. Numerical verification of the results leads to the conclusion that the planar and annular flows of Ellis and power law fluids are qualitatively similar. The quantitative differences resulting from the slit curvature and the type of constitutive equation are relatively large only for flows of strongly non-Newtonian liquids.