This article presents di¤erent parameter estimation methods for ‡exible Weibull distribution introduced by Bebbington et al. (Reliability En- gineering and System Safety 92:719-726, 2007), which is a modi…ed version of the Weibull distribution and is suitable to model di¤erent shapes of the hazard rate. We consider both frequentist and Bayesian estimation methods and present a comprehensive comparison of them. For frequentist estima- tion, we consider the maximum likelihood estimators, least squares estima- tors, weighted least squares estimators, percentile estimators, the maximum product spacing estimators, the minimum spacing absolute distance estima- tors, the minimum spacing absolute log-distance estimators, Cramér von Mises estimators, Anderson Darling estimators, and right tailed Anderson Darling estimators, and compare them using a comprehensive simulation study. We also consider Bayesian estimation by assuming gamma priors for both shape and scale parameters. We use a Markov Chain Monte Carlo algorithm to compute the posterior summaries. A real data example is also a part of this work.