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The mean-square wave response of a lightly damped thermo-viscoelastic medium to a special type of nonstationary random excitation is deter mined. The excitation function on the thermo viscoelastic medium is taken in the form of a pro duct of a well defined, slowly varying envelope function, and a part which prescribes the statistical characteristics of the excitation. The rectangular step function is used for the envelope function, and noise with an exponentially decaying harmonic correlation function is used to prescribe the statistical property of the excitation. By taking into consideration the slow variation envelope function and the wave characteristics of the lightly damped thermoviscoelastic medium, the mean square response is evaluated by using F.F.T.