The settling of solid particles in a liquid due to centrifugal force is described by using the equations of one-dimensional unsteady two-phase flow. By neglecting the acceleration terms the momentum equation can be reduced to a functional relationship between the dependant variables of the problem (volumetric concentration α of the solid particles and volumetric flux j). As an additional relation for the unknown quantities, a first order partial differential equation is obtained from the equation of continuity for the solid particles. Concentration jumps (e.g. discontinuities between suspension and clear liquid or sediment) are described as kinematic shock waves. Analytical solutions are obtained for the kinematic wave fronts and for certain cases of shock waves. The results for the centrifugation process with uniform particle size show that several cases are to be distinguished. Under certain conditions the concentration of the suspension depends on time only and not on the radial coordinate of the rotating system. Other initial conditions give additional discontinuities within the suspension.