We implemented an iterative nonrigid registration algorithm to accurately combine functional (PET) and anatomical (MRI) images in 3D. Our method relies on a Finite Element Method (FEM) and a set of fiducial skin markers (FSM) placed on breast surface. The method is applicable if the stress conditions in the imaged breast are virtually the same in PET and MRI. In the first phase, the displacement vectors of the corresponding FSM observed in MRI and PET are determined, then FEM is used to distribute FSM displacements linearly over the entire breast volume. Our FEM model relies on the analogy between each of the orthogonal components of displacement field, and the temperature distribution field in a steady state heat transfer (SSHT) in solids. The problem can thus be solved via standard heat-conduction FEM software, with arbitrary conductivity of surface elements set much higher than that of volume elements. After determining the displacements at all mesh nodes, moving (MRI) breast volume is registered to target (PET) breast volume using an image-warping algorithm. In the second iteration, to correct for any residual surface and volume misregistration, a refinement process is applied to the moving image, which was already grossly aligned with the target image in 3D using FSM. To perform this process we determine a number of corresponding points on each moving and target image surfaces using a nearest-point approach. Then, after estimating the displacement vectors between the corresponding points on the surfaces we apply our SSHT model again. We tested our model on twelve patients with suspicious breast lesions. By using lesions visible in both PET and MRI, we established that the target registration error is below two PET voxels. The surface registration error is comparable to the spatial resolution of PET.