In this paper, innovative models for analysis of survival data, indexed by two shape parameters, which encompasses a wide range of situations are discussed. These models are called hypertabastic survival models. The models are shown to provide different shaped hazard rates. One of the unique strengths of the hypertabastic models is the flexibility of the hazard function that permits the data to determine the nature of the hazard function without its being inadvertently imposed through the selection of improper models. The consideration of the different hazard shapes explains the different mechanisms of the outcome behavior. This helps researchers understand the outcome status over time.