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• Semi-analytical approach presenting derivation of the scattering matrix related to the region with adhesively bonded joint. • Effect of the energy balance convergence of local sub-waveguide sections on the global scattering matrix. • Effect of the number of considered complex wavenumbers entering the computational process on the predicted results accuracy. Problems related to scattering phenomena of the antisymmetric fundamental Lamb wave mode with an adhesively bonded lap joint containing a disbond in the adhesive layer is being solved within the framework of this paper. Overall, two methods are used in order to identify energy scattering coefficients of reflected as well as transmitted Lamb waves. These methods include a hybrid approach, which incorporates the finite element method (FEM) with general orthogonality relation, and semi-analytical approach, combining the modal expansion technique and orthogonal property of Lamb waves. With the use of the stress and displacement continuity condition on selected interfaces, it is possible to explicitly derive the global scattering matrix, containing the information related to the scattering process of present Lamb wave modes in a given geometry. Both approaches are then adopted on three configurations of the adhesively bonded lap joint in terms of the length of the disbond, which is then positioned within the overlapped region. The obtained results, among others, clarify the relationship between geometric parameters of the region containing the overlapping with the horizontal disbond and the role of non-propagating modes in the computational process of energy scattering coefficients of propagating modes. [ABSTRACT FROM AUTHOR]