Abstract We present a super-fast and parameter-free algorithm for non-rigid elastic registration of images of a serially sectioned whole rat brain. The purpose is to produce a three-dimensional high-resolution reconstruction. The registration is modelled as a minimization problem of a functional consisting of a distance measure and a reg- ularizer based on the elastic potential of the displacement ¯eld. The minimization of the functional leads to a system of non-linear partial di®erential equations, the so-called Navier-Lam¶e equations (NLE). Discretization of the NLE and a ¯xed point type iteration method lead to a linear system of equations, which has to be solved at each iteration step. We not only present a super-fast solution technique for this system, but also come up with sound strategies for accelerating the outer iteration. This does include a multi-scale approach based on a Gaussian pyramid as well as a clever estimation of the material constants for the elastic potential. The results of the registration process were controlled by an expert who was able to recognize histological details like lamina- tions which was not possible before. Therefore, it is essential to apply elastic registration to this kind of imaging problem. Finally, the visually pleasing results were quanti¯ed by a distance measure leading to an improvement of about 79% after just 35 iteration steps.