In this paper, Propagated modes in a three-layer adhesive joint are investigated regardless of wave generation source influence and also by taking into consideration it and low-attenuation modes are determined. In the beginning, lamb wave propagation in the adhesive joints is investigated using global matrix method and characteristic equation is derived by applying continuity and boundary conditions which are included traction-free boundary conditions on outer surfaces of the joints and continuity between layers. Phased velocity and attenuation dispersion curves in terms of frequency are obtained by numerical solution of the characteristic equation. Then, the source influence on wave field is investigated using normal mode expansion method. Average power flow of low-attenuation excited mode and its energy percent to the lamb wave total energy curves in terms of source parameters for specific frequency are obtained. These results are used to determine the suitable parameters of the source which are used to generate low-attenuation lamb wave mode. Finally, finite element simulation of lamb wave generation is performed to compare with the results of normal modes expansion method. The results indicate to generate M3 mode with low-attenuation level in the three-layer adhesive joint aluminium-epoxy-aluminium at frequency 0.25 MHz, suitable wedge angle is 16 degree and suitable transducer width is 20 mm.