The present study is concerned with developing some statistical models to evaluate and analyze software reliability. We have developed the analytical structure of the logistic model to be used for testing and evaluating the reliability of a software package. The proposed model has been shown to be useful in the testing and debugging stages of the developmental process of a software package. It is important that prior to releasing a software package to marketing that we have achieved a target reliability with an acceptable degree of confidence. The proposed model has been evaluated and compared with several existing statistical models that are commonly used. Real software failure data was used for the comparison of the proposed logistic model with the others. The proposed model gives better results or it is equally effective. The logistic model was also used to model the mean time between failure of software packages. Real failure data was used to illustrate the usefulness of the proposed statistical procedures. Using the logistic model to characterize software failures we proceed to develop Bayesian analysis of the subject model. This modeling was based on two different difference equations whose parameters were estimated with Bayesian regressions subject to specific prior and mean square loss function.