This paper is concerned with the Bayesian estimation problem of the unknown parameters of the compound Weibull model with unequal shape parameter. A Bayesian estimates are obtained for the uniform and gamma prior probability densities assuming independent prior distributions. Bayesian results in the case of compound Weibull model with equal shape parameter and in the case of one cause obtained as of failure models can be a special case from our results. Numerical comparison between the maximum likelihood and Bayes'estimates has been carried out using random numbers and computer facilities. We observed that most of the Bayes'estimates are more efficient than the maximum likelihood estimates.