The paper investigates the response of a magnetorheological (MR) fluid based mount that combines the squeeze and flow modes in operation. The mount governing equations are introduced and the effect of system parameters on its performance is analyzed. The proposed design yields a high static and a low dynamic stiffness in the working frequency range of the mount. The overall vibration isolation characteristic of the mount is enhanced if compared to that of existing hydraulic mounts. Displacement and/or force transmissibility can be isolated or significantly reduced, in real time, by controlling the MR fluid yield stress. An embedded electromagnet is used to activate the MR fluid that can work in either squeeze or flow modes, or in both simultaneously. The results indicate that the flow mode is less effective in reducing transmissibility than the squeeze mode. However, when the flow and squeeze modes are both activated, the effect of the flow mode becomes more obvious.