Tagged cardiac magnetic resonance (MR) imaging can non-invasively image deformation of the left ventricular (LV) wall. Three-dimensional (3D) analysis of tag data requires fitting a deformation model to tag lines in the image data. In this paper, we present a 3D myocardial displacement and strain reconstruction method based on a B-spline deformation model defined in prolate spheroidal coordinates, which more closely matches the shape of the LV wall than existing Cartesian or cylindrical coordinate models. The prolate spheroidal B-spline (PSB) deformation model also enforces smoothness across and can compute strain at the apex. The PSB reconstruction algorithm was evaluated on a previously published data set to allow head-to-head comparison of the PSB model with existing LV deformation reconstruction methods. We conclude that the PSB method can accurately reconstruct deformation and strain in the LV wall from tagged MR images and has several advantages relative to existing techniques.