Compression-assisted magnetorheological (MR) fluid strengthening at the nonconfined conditions was studied with the Anton Paar Physica MCR300 magnetorheometer adapted for measurements of the storage modulus of magnetized MR fluid after its exposure to compressive strains as well as for measurements of the shear stress during build-up of compression at different mutual field/compression orientations. It was found that the compression significantly increases the linear viscoelastic region, suggesting an essential enhancement in the elastic properties of the tested material. An elevated elasticity of MR fluid compressed normal to the field is observed. Build-up of compression of magnetized MR fluid results in a dramatic increase in the shear stress and occurs in two phases. It is suggested that in the first phase, at the low compressive strains, the increase in the stress is associated with the elastic deformation of the initial structure formed by a magnetic field. Subsequent increase in the shear stress in the second phase is attributed to the compression-assisted MR fluid strengthening, which takes place when the compressive strain increases beyond the elastic region and the initial chain structure gradually transforms into a structure of a thick and strong columns. Compression normal to the field results in significantly higher shear stress increment than imposed along it. (C) 2016 The Society of Rheology.