<p>A mathematical model of the flow and separation of two-phase non-Newtonian media in curvilinear regions used in centrifugal separators to intensify the separation process is constructed. The equations for conservation of mass and momentum of the two-phase medium, written in the quasi-homogeneous approximation, are solved using the method of equal flow-rate surfaces. An algorithm for numerically calculated settling of dispersed particles is developed, taking into account the variability of the settling path length and the direction of centrifugal force relative to the walls of a curved channel. Numerical calculations are performed for parabolic and conical channels, taking into account the presence of an initial flow section for various properties of the medium and particles. A computational experiment was conducted to study various flow regimes in the channel and the separation process of a two-phase medium depending on its rheological properties for the Ostwald–de Waele law of state. The shape of the flow velocity profile and the trajectory of particle motion are significantly affected by the coefficient of its nonlinearity and the speed of rotation of the channel around the axis of symmetry.</p>