A three-dimensional (3-D) elastic registration algorithm has been developed to find a veridical transformation that maps activation patterns from functional magnetic resonance imaging (fMRI) experiments onto a 3-D high-resolution anatomical dataset. The proposed algorithm uses trilinear Bézier-splines and a 3-D voxel-based optimization technique to determine the transformation that maps the functional data onto the coordinate system of the anatomical dataset. Simple conditions are presented which guarantee that the data are mapped one-to-one on each other. Two voxel-based similarity measures, the linear correlation coefficient and the entropy correlation coefficient, are used. Their performance with respect to the registration of fMRI data is compared. Tests on simulated and real data have been performed to evaluate the accuracy of the method. Our results demonstrate that subvoxel accuracy can be achieved even for noisy low-resolution multislice datasets with local distortions up to 10 mm. Although the method is optimized for the registration of functional and anatomical MR images, it can also be used for solving other elastic registration problems.