Abstract: This paper proposes a differential geometric framework for nonlinear models for Failure Time Data. The framework may be regarded as an extension of that presented by Bates \& Wates for nonlinear regression models. As an application, we use this geometric framework to derive three kinds of improved approximate confidence regions for parameter and subset parameter in terms of curvatures. Several results such as Bates and Wates (1980), Hamilton (1986) and Wei (1998) are extended to our models.