This paper is concerned with an investigation of the rheological performance of magnetorheological fluids under squeeze flow. Preliminary results on Newtonian fluids are first compared to Stefan's equation. Then, unidirectional monotonic compression tests are carried out in the presence of uniaxial external magnetic fields at slow compression rates under constant volume operation. Results are compared to Bingham plastic, biviscous, and single chain micromechanical squeeze flow models. Measurements using combined deformation modes (compression+small-strain oscillatory shear) suggest a compression-induced shear strengthen effect up to strains of similar to 0.5. Particle-level dynamic simulations are in qualitatively good agreement with experimental observations. (C) 2011 The Society of Rheology. [DOI: 10.1122/1.3574932]