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The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are successfully developed to solve electrically very large sized perfectly electric conducting (PEC) objects. Using the impedance boundary conditions (IBC) the integral equations can be simplified and solved for wave problems involving imperfectly conducting surfaces. Thus, the algorithm is firstly implemented and verified by comparing with the exact analytical solution for a PEC sphere, and then extended for imperfectly conducting (thin material coating) objects and verified with the analytical solution. Subsequently, it has been applied to an aircraft model with both PEC and material coating surface the results and compared.