We introduce a coupled finite and boundary element method for elastic-plastic analysis over multiscale electronic packaging structures. Based on the FE-BE coupling algorithm, an automatic implementation procedure for the coupling of the Abaqus with a self-written elastic BE code is introduced for elastic problems. In the mixed FEM-BEM model, the effective stiffness and effective forces at the interfacial boundary are evaluated by the self-written BE code. Then, the obtained effective stiffness and effective forces are assembled to the global FE formulations by using the user subroutine (UEL) in Abaqus. Numerical simulation of structures with plastic deformation, stress concentration, etc. is carried out by using FEM theory. The boundary element method is used for linear elastic domains with large-scale structure. The proposed method offers several key improvements compared with current analysis methods available for multi-scale electronic packaging structures. The benefits are: (i) the powerful pre- and post-processing of ABAQUS; (ii) the higher accuracy of the solution; (iii) the computational cost and time can be reduced by using the scheme; and (iv) solving systems with infinite extension by using the BEM as a supplement. Furthermore, we demonstrate the ability of the proposed approach to handle multiscale structures in electronic packaging problems.