The acoustic damping for single modes of a finite rectangular panel, simply supported in an infinite baffle, is theoretically determined from the ratio of the acoustic energy radiated per cycle to the vibratory energy of the panel. Asymptotic solutions for the low‐frequency region are presented for a panel mode driven at an arbitrary frequency and for a panel mode vibrating at its natural frequency. Curves of acoustic damping for a panel mode vibrating at resonance, as a function of the panel thickness‐to‐length ratio, are presented for various panel aspect ratios. For panels vibrating below the critical frequency, the damping depends on the aspect ratio with square panels developing the smallest value. For panels vibrating above the critical frequency, the damping is nearly independent of the aspect ratio.