A modeling method is proposed for the acoustic analysis of a three-dimensional (3D) rectangular opened enclosure coupled with a semi-infinite exterior field by a rectangular opening of arbitrary size, and with general wall impedance. In contrast to existing modeling methods that solve the differential equations, the energy principle in combination with a 3D modified Fourier cosine series is employed in the present method for the modeling of this system. Under this theoretical framework, the effect of an opening in the wall of a rectangular enclosure is taken into account via the work done by the sound pressure acting on the opening between the finite enclosure and exterior domain. The sound pressure inside the opened enclosure is expressed as the combination of a 3D trigonometric cosine series and one supplementary 2D expansion introduced to ensure uniform convergence of the solution over the entire solution domain including opening boundary. The acoustic responses of the opened enclosure are obtained based on the energy expressions for the enclosure system. The effectiveness and reliability of the current method are checked against the results obtained by the boundary element method and experimental results, and excellent agreement is achieved. The effects of sizes and positions of the opening and wall impedance on the acoustic behaviors of opened enclosure system are investigated.