In the present paper tensile stresses perpendicular to the grain in reinforced double-tapered beams made of glued laminated timber are discussed. The beams are analysed using the finite element method within the linear elasticity theory with the influence of orthotropic material properties. The main objective is to assess the influence of transverse reinforcement on the values and distributions of the analysed stresses and to identify the most efficient scheme of reinforcement. The obtained results prove that, with the use of the proposed tools, it is possible to assess the level of stress, including delaminating stress, and to indicate the areas of occurrence of such stress with high precision.