The switching characteristics and the magnetization-flop behavior in magnetic tunnel junctions exchange biased by synthetic antiferromagnets (SyAFs) are investigated by using a computer simulations based on a single-domain multilayer model. The bias field acting on the free layer is found to be sensitive to the thickness of neighboring layers, and the thickness dependence of the bias field is greater at smaller cell dimensions due to larger magnetostatic interactions. The resistance to magnetization flop increases with decreasing cell size due to increased shape anisotropy. When the cell dimensions are small and the synthetic antiferromagnet is weakly, or not pinned, the magnetization directions of the two layers sandwiching the insulating layer are aligned antiparallel due to a strong magnetostatic interaction, resulting in an abnormal magneto resistance (MR) change from the high-MR state to zero, irrespective of the direction of the free-layer switching. The threshold field for magnetization-flop is found to increase linearly with increasing antiferromagnetic exchange coupling in the synthetic antiferromagnet. Irrespective of the magnetic parameters and cell sizes, magnetization flop does not exist near zero applied field, indicating that magnetization flop is driven by the Zeeman energy.