This paper presents the formulation of strain-based finite elements for modelling composite beams with finger joints considering slip between the layers. The finite elements are derived according to Reissner beam theory based on the modified principle of virtual work where the displacements and rotations are eliminated from the problem and the axial deformation, shear deformation and curvature of the layers remain only functions to be approximated within the finite element. Lagrange polynomials are used as shape functions to approximate the deformations and various interpolation methods are applied to numerical examples, with the Lobatto integration scheme giving slightly better results than Equidistant. The experimentally measured mechanical properties needed as input data for the numerical model are given for the four glued laminated beech beams. The numerical model is thoroughly verified and validated. The results show that the presented finite element formulation is an efficient tool for practical and accurate calculations. •New finite elements for composite beams with slip and finger joints are proposed.•Numerical model is validated and verified with experimental results.•The finite elements exhibit no slip and shear locking.