Comparing Ultrasound Computer Tomography (USCT) to the well-known Magnetic Resonance Imaging (MRI) is an essential step in evaluating the clinical value of USCT. Yet the different conditions of the breast either embedded in water (USCT) or in air (MRI) prevent direct comparison. In this work we compare two strategies for image registration based on biomechanical modeling to automatically establish spatial correspondence: a) by applying buoyancy to the MRI, or b) by removing buoyancy from the USCT. The registration was applied to 9 datasets from 8 patients. Both registration strategies revealed similar registration accuracies (MRI to USCT: mean = 5.6 mm, median = 5.6 mm, USCT to MRI: mean = 6.6 mm, median = 5.7 mm). Image registration of USCT and MRI allows to delineate corresponding tissue structures in both modalities in the same or nearby slices. Our preliminary results indicate that both simulation strategies seem to perform similarly. Yet the newly developed deformation of the USCT volume is less computationally demanding: As the breast is subjected to buoyancy it can thereby serve as the unloaded state while for the contrary strategy we have to solve an inverse problem.