An existing beam-on-elastic-foundation (BEF) model was used to determine the perpendicular-to-grain tensile stresses in timber members subjected to loading parallel to the grain by bolted connections. A set of relatively simple equations for the analysis of a Timoshenko beam of finite length on a Winkler foundation is given, and appropriate foundation stiffness values are discussed. While previous applications of the model have associated the foundation stiffness with the perpendicular-to-grain elastic strain in the timber, it is suggested that a fracture layer be introduced and the foundation stiffness be associated with the perpendicular-to-grain tensile strength and the mode I fracture energy of the wood. The latter estimation of the foundation stiffness, which leads to a so-called ‘quasi-non-linear fracture mechanics model’, has been applied with success to other problems where the BEF model has been used for the analysis of mode I fracture. An existing model for the analysis of the pure mode II fracture, which is also a quasi-non-linear fracture mechanics model based on similar assumptions as the proposed model for analysis of the mode I fracture, is reviewed. A simple way of handling mixed-mode fracture problems by means of the simple empirical interaction of the proposed pure mode I and pure mode II quasi-non-linear fracture mechanics models is discussed.