This work presents results of a comprehensive analysis of the Lenz effect due to motion of artificial heart valves during magnetic resonance imaging. The interaction of rotating metallic heart valves with magnetic fields is studied by performing a time-domain analysis of the corresponding electromagnetic problem. We applied the finite element method (FEM) to solve the T - Omega formulation of Maxwell equations in two cases: first, for metallic disks located in the high intensity homogenous field of the magnet iso-center, and second, disks located in the non-uniform fringe field of the bore entrance. We showed that for valves with full solid disks (such as Starr-Edwards 6500) located in the magnet iso-center, the magnitude of adverse forces can be comparable to the forces applied by the beating heart. However, for rings which consist of multiply connected conductive regions, skin effect and proximity effect counteract, which leads to a diminished magnetic force. Results of this study show that mechanical heart valves with strengthening rings may be considered safe even under ultra-high imaging conditions with field intensities as high as 10 T. However, heart valves with full conducting disks should be considered as a contraindication to MR imaging.