The study experimentally examines the quasi-static shear deformation of a magnetorheological (MR) fluid structured in an external magnetic field. Experiments are carried out using a rheometer with a plate–plate configuration. The working surfaces of the measuring geometry are modified to demonstrate their influence on the response of the field-structured MR fluid. The simplest possible suspension of microparticles of carbonyl iron in mineral oil without using surfactants or any modifiers is used. The difference in results obtained for structured MR fluid with different concentrations of magnetic particles using different modifications of the surface is demonstrated. The results are intended to motivate more intensive research on the issue and further more in-depth theoretical analysis of static elastic properties of structured MR fluids. Certain related critical issues are briefly highlighted.