Experimental and theoretical studies of the response of integrally stiffened skin structures to random acoustic pressures are described. Typical structures are lightly damped and show significant response in the frequency range 100 to 2000 Hz. Some methods of increasing the damping are described and experimental results quoted. In the most efficient system investigated a damping treatment adding only 2 percent by weight to the structure reduced the rms stress by a factor of approximately three for the case of broad band excitation having a constant spectral density in the range 100 to 1000 Hz.