The study investigates the performance of a semi-active vehicle engine mount incorporating an MR damper working in the squeeze mode (MRSQD), summarising its design, operating principles and key characteristics. The mathematical model of the mount is formulated based on the newly developed MRSQD. Two control algorithms are proposed for MRSQD control. The first algorithm (ALG1) uses the inverse model of the engine-frame system, the other is the sliding mode algorithm (ALG2). The effectiveness of the engine mount system is demonstrated in computer simulation.