The response and energy dissipation of rock under stochastic stress waves were analyzed based on dynamic fracture criterion of brittle materials integrating with Fourier transform methods of spectral analysis When the stochastic stress waves transnut through rocks,the frequency and energy ratio of harmonic components were calculated by analytical and discrete analysis methods.The stress waves in shale, malmstone and liparite were taken as examples to illustrate the proposed analysis methods.The results show the harder the rock, the less absorption of energy,the more the useless elastic waves transmitting through rock, and the narrower the cutoff frequency to fracture rock.When the whole stress energy doubles either by doubling the duration time or byincreasing the amplitude of stress wave, ratio of the energy of elastic waves transmitting through rock to me whole stress energy (i.e.energy dissipation ratio)is decreased to 10%-15%. When doubling the duration time.the cutoff frequency to fracture rock remains constant.However, with the increase of the amplitude of stress wave. the cutoff frequency increases accordingly.