We describe a new algorithm for non-rigid registration capable of estimating a constrained dense displacement field from multi-modal image data. We applied this algorithm to capture non-rigid deformation between digital images of histological slides and digital flat-bed scanned images of cryotomed sections of the larynx, and carried out validation experiments to measure the effectiveness of the algorithm. The implementation was carried out by extending the open-source Insight ToolKit software. In diagnostic imaging of cancer of the larynx, imaging modalities sensitive to both anatomy (such as MRI and CT) and function (PET) are valuable. However, these modalities differ in their capability to discriminate the margins of tumor. Gold standard tumor margins can be obtained from histological images from cryotomed sections of the larynx. Unfortunately, the process of freezing, fixation, cryotoming and staining the tissue to create histological images introduces non-rigid deformations and significant contrast changes. We demonstrate that the non-rigid registration algorithm we present is able to capture these deformations and the algorithm allows us to align histological images with scanned images of the larynx. Our non-rigid registration algorithm constructs a deformation field to warp one image onto another. The algorithm measures image similarity using a mutual information similarity criterion, and avoids spurious deformations due to noise by constraining the estimated deformation field with a linear elastic regularization term. The finite element method is used to represent the deformation field, and our implementation enables us to assign inhomogeneous material characteristics so that hard regions resist internal deformation whereas soft regions are more pliant. A gradient descent optimization strategy is used and this has enabled rapid and accurate convergence to the desired estimate of the deformation field. A further acceleration in speed without cost of accuracy is achieved by using an adaptive mesh refinement strategy.