An approach to the calculation of drag and fall velocity of a spherical particle in generalized Newtonian and viscoplastic fluids is suggested. It is based on the application of the modified Rabinowitsch-Mooney equation together with the corresponding relations for consistency variables. The usefulness of this approach has been verified for the Ellis and Bingham fluids. The solution has been used to suggest the corresponding relationships for the calculation of pressure drop in the flow of a viscoplastic fluid through a random fixed bed of particles.