The effect of unbalanced magnetic pull (UMP) caused by air gap eccentricity on the vibration of a permanent magnet synchronous motor (PMSM) is investigated. The force model is established analytically by the Maxwell stress method. For accurate consideration of the eccentricity condition, mixed eccentricity, axial-varying eccentricity, and eccentricity caused by motor frame vibration are modeled and combined. The model of the rotor-bearing system, which includes the UMP model, is developed with two different methods. In the first method, UMP is added as a linear negative spring to the rotor model, whereas in the second method, UMP is included as an external force. The rotor system of a centrifugal pump driven by an integrated PMSM is modeled using beam elements, and the two distinct modeling approaches for UMP are applied. From the results, the UMP effect on vibration and the difference between the two modeling methods are investigated. To verify the results of the analysis, experimental work is done with a pump test rig, and results of frequency spectra are obtained. Based on the analyses and experimental work, the negative stiffness effect and additional vibration excitations caused by UMP are examined.