This study presents a new approach for flow analysis of magnetorheological (MR) fluids through channels with various surface topologies. Based on an experimental study an analytical method is developed to predict the pressure loss of a MR fluid as a function of the applied magnetic field strength, volumetric flow rate, and surface topology, without utilizing the concept of shear yield stress. A channel flow rheometer with interchangeable channel walls is built to demonstrate that the pressure loss across the MR fluid flow channel is significantly affected by the channel surface properties. Based on the experimental study it is concluded that a unique shear yield stress cannot be defined for a given MR fluid, since its pressure drop depends on the surface topology of the device. Therefore, a relation for nondimensional friction factor associated with MR fluid channel flow is developed in terms of a modified Mason number and dimensionless surface topology parameters. Using the nondimensional model, the pressure loss for various magnetic fields and volumetric flow rates can be represented by a single master curve for a given channel surface topology without the assumption of a constitutive model for MR fluids.