This paper presents a method for an estimation of the axis of rotation of radially symmetric objects from their fragments. In particular, fragments of archaeological pottery are considered. The method exploits basic geometrical properties of fragments which are described by an appropriate model. The estimation is performed in several steps which continuously improve accuracy and robustness of an initial estimate. Because only coordinates of surface points of a fragment are required for the estimation, the proposed method can be implemented as a fully automatic process. The approach has been evaluated on both synthetic objects and real pottery fragments.