In this paper, a method for analyzing flutter for a turbomachinery row with aerodynamically coupled structural modes is presented. The majority of observed turbomachinery flutter incidents involve only one structural mode family due to high mass ratio, high solidity and significant natural frequency separation for blades of traditional design. However, with the trend of higher aerodynamic loading, the wide usage of light weight composite materials and lower blade counts, the likelihood of coupled-mode flutter increases, particularly for turbofans or open rotors. Under such circumstances, the widely used energy method for flutter analysis is not valid. To model this situation, a novel aeroelastic eigenvalue method that is capable of modeling both single- and coupled-mode flutter is proposed. This method takes into account the aerodynamic coupling effects between different vibration modes through the influence coefficient cross sub-matrices, which can be efficiently computed by a harmonic balance solver. The new method is efficient as the required computational effort is only two times that of the traditional single mode analysis approach. The new method is demonstrated and validated by presenting results for Standard Configuration Eleven and NASA Rotor 67 flutter test cases in this paper.