The coupled flutter problem of long-span bridges using complex notation offering simplicity and robustness is addressed in this paper. Firstly, both consistent and lumped aerodynamic matrix of a bridge deck element are presented for the Scanlan's linear self-excited forces included 18 dimensionless aerodynamic derivatives considering vertical bending, pitching torsion as well as lateral bending. Secondly, both the multi-mode and full-mode flutter analysis methods employ the general expression of the linear unsteady aerodynamic forces. The full-mode method adopts the most effective eigensolution technique based on the generalized eigenvalue problem (GEP) formulated in the state space is conducted to find the critical wind speed by an incremental-iterative procedure, in which all vibration modes of the bridge are considered. Several study cases shown that the predictions of the onset flutter given by proposed method are compared with those obtained by existing methods. Both lumped formulation in terms of structural mass and aerodynamic force may provide lower critical velocities at flutter.