In this two-part research project the inelastic properties of a selected group of magnetorheological composites under cyclic shear have been identified. Composites whose matrices were elastic porous structures with pores filled with a magnetorheological fluid were investigated. The composite materials’ functional properties are similar to those of magnetorheological fluids. But, as opposed to the fluid alone, the composite’s geometry and dimensions can be freely shaped. Owing to this, the costs can be reduced and the applicability can be extended. In the literature on the subject such composites are also referred to as magnetorheological fluid impregnated solids. In the first part of this work an overview of smart magnetic materials is presented. Then the originally fabricated composite, consisting of a matrix and a filling fluid, is described. The test stand, including a system of control, acquisition and processing of measuring (mechanical and magnetic) signals, is presented. The experimentally determined hysteresis loops for cyclic shear are used in the second part of this research project to identify constitutive models.