The vibration of a simply supported rectangular plate with a discretely attached mass and fluid radiation loading is considered. The equations of motion are solved by utilizing theinvacuoeigenfunctions of a homogeneous panel as the basis for Fourier decomposition of both the fluid loading and attached mass loading. A modal matrix equation is established for the interactive system which includes the cross‐modal coupling induced by the discrete mass and acoustic fluid. The solution is exemplified by the numerical investigation of a centrally excited plate with a concentrated mass at center and off‐center locations. The influence of mass attachment upon both the plate response and radiated pressure is illustrated.