Slug tests are one of the most common field methods for estimating local hydraulic conductivity, for fast and low-cost characterization of aquifer heterogeneity. In highly permeable zones, underdamped responses, identified by oscillations of the water level, are generally observed. Several analytical solutions have been developed for modeling underdamped slug test responses. Interpreting these tests in fractured rocks can be challenging due to system complexity, which ultimately raises questions about the appropriate model for interpreting a given dataset. In order to obtain insights on this fundamental problem for slug test analyses in fractured rocks, a complete evaluation on three transient solutions for linear, radial and spherical flow configuration extended to include inertial and wellbore skin effects in a fully penetrating well is proposed. A first comparison between these transient solutions and the classical steady-state model shows that, in some cases, the latter may underestimate hydraulic conductivity. Next, parameter sensitivity and uncertainty analyses were conducted on each solution to evaluate the classical problem of non-uniqueness between models and parameters. As expected, the results from sensitivity analysis show that the hydraulic conductivity parameter is the most sensitive regardless of model configuration. For specific storage, sensitivity is important for the linear model, moderate for the radial model and negligible for the spherical model. For the skin factor, however, sensitivity is negligible for the linear model, moderate for the radial model and most important for the spherical model. These results were next confirmed by performing Bayesian inferences using Markov Chain Monte Carlo technique to evaluate uncertainty on each parameter. Uncertainties appear significant for negligibly sensitive parameters but nearly insignificant for the most sensitive parameters. For all flow configurations, hydraulic conductivity appears however to be accurately estimated. Examples of interpretations for data collected in fractured rocks illustrate the application of these models and provide some recommendations.