This paper introduces a non-contact method for the identification, quantification, and documentation of fibre direction of European beech wood (Fagus sylvatica L.). The developed approach is based on an automated visual analysis of the spindle pattern formed by the medullary rays, also termed wood rays. Each spindle is identified by means of image analysis technique, its position and orientation is determined, and the fibre direction of discretised elements is calculated. The individual process steps necessary to obtain an estimate of the fibre direction of a board are explained using the examples of five different failure types. In all examples, the estimated fields of fibre direction are congruent with the actual fibre direction determined by means of (1) the orientation of all present shrinkage cracks, which are established indicators for the fibre direction in wood, and (2) the fracture pattern after tensile testing. Employing the presented approach could open up new possibilities for the characterisation of European beech and other hardwood species with multi-row medullary rays in several fields of application, in particular regarding stress grading.