Summary: This article outlines flexible strategies to model survival curves for censored data and find parametric confidence intervals using generalised lambda distributions. Owing to the rich shapes of generalised lambda distributions, these distributions are well suited to the problem of estimating survival curves. This article presents three useful techniques in estimating survival curves: matching partial probability weighted moments (PWM), maximum likelihood estimation (MLE) and simulation-refitting (SR) methods. The performance of these techniques are examined using right skewed, left skewed, symmetric bell curved and extreme value simulated data with varying degrees of censoring and sample sizes. Applications of the proposed methods in the context of multi-stage disease modelling and competing risks are also provided. Under controlled simulated experiments, PWM and MLE estimation tend to exhibit more precise estimates for survival curves than the SR method, however, the SR method tends to perform better in practice. The methods proposed in this article are very general and can be used to fit a wide range of empirical survival curves. Compared to the standard Kaplan Meier survival curve, the methods in this article have the added benefits of producing smoother survival curves and more consistent statistical estimates where all the statistical information of the survival curve can be obtained directly under one parametric model.