A computational method to predict speech intelligibility in noisy environments has been developed. By modeling speech and noise as stochastic signals, the information transmission through a given auditory model can be estimated. Rate-distortion theory is then applied to predict speech recognition performance. Results are compared with subjective tests on normal and hearing impaired listeners. It is found that the method underestimates the supra-threshold deficits of hearing impairment, which is believed to be due to an overly simple auditory model and a small dictionary size.