Periodically corrugated thin metal films have an interesting property such as the partial or total resonance absorption of incident light energy. The resonance absorption is asso- ciated with the excitation of the surface plasmons and is then termed the resonance absorption. Most of studies on the resonance absorption have mainly dealt with a thin metal film grating whose surfaces are periodic in one direction. We investigate the plasmon resonance of a multilayer- coated bigrating which consists of thin-films corrugated periodically in two directions. In solving the problem, we employed a computational technique based on modal expansion. Taking a sand- wiched structure Vacuum/Ag/SiO2 /Ag/Vacuum for an example, we observed: (1) excitation of a SISP mode at the lit surface of the 1st Ag layer with strong field enhancement for thick enough Ag layer case; (2) excitation of coupled SPR modes (SRSP or LRSP) at each surface between vacuum and Ag layers with strong field enhancements for thin enough Ag layer cases no matter with the thickness of SiO2 layers; (3) standing wave pattern of the electric filed in the SiO2 film. The coupled plasmon modes were resulted by the resonance waves excited on four surfaces in these cases.