During breast conserving surgery (BCS), magnetic resonance (MR) images aligned to accurately display intraoperative lesion locations can offer improved understanding of tumor extent and position relative to breast anatomy. Unfortunately, even under consistent supine conditions, soft tissue deformation compromises image-to-physical alignment and results in positional errors. A finite element inverse modeling technique has been developed to nonrigidly register preoperative supine MR imaging data to the surgical scene for improved localization accuracy during surgery. Registration is driven using sparse data compatible with acquisition during BCS, including corresponding surface fiducials, sparse chest wall contours, and the intra-fiducial skin surface. Deformation predictions were evaluated at surface fiducial locations and subsurface tissue features that were expertly identified and tracked. Among n = 7 different human subjects, an average of 22 ± 3 distributed subsurface targets were analyzed in each breast volume. The average target registration error (TRE) decreased significantly when comparing rigid registration to this nonrigid approach (10.4 ± 2.3 mm vs 6.3 ± 1.4 mm TRE, respectively). When including a single subsurface feature as additional input data, the TRE significantly improved further (4.2 ± 1.0 mm TRE), and in a region of interest within 15 mm of a mock biopsy clip TRE was 3.9 ± 0.9 mm. These results demonstrate accurate breast deformation estimates based on sparse-data-driven model predictions. The data suggest that a computational imaging approach can account for image-to-surgery shape changes to enhance surgical guidance during BCS.