Transrectal ultrasound (TRUS) guided needle biopsy is currently the clinical routine for diagnosis of prostate cancer. Due to the blurry TRUS imaging, magnetic resonance imaging (MRI) of prostate is usually taken prior to the biopsy procedure to assist needle target planning. In this paper, a novel geometric transformation method, which is based on the mechanics of materials, is proposed to facilitate the deformable registration of lesion sites from MRI to ultrasound imaging. In the method an enlarged shell, scaled from the geometry of prostate constructed from ultrasound imaging, is used to squeeze the prostate constructed from MRI imaging. The prostate can automatically rotate and position itself towards the target geometry, and deforms to match the target throughout the entire volumes. Transformations of 3D volumes as well as 2D sections of prostate are carried out to evaluate the transformation performance with respect to different material properties and segmentation errors. Some practical issues on applying the method to clinical biopsy operations are discussed. We show that this FEM based transformation method is promising in deformable registration and could be used in other organ image registrations.