Simulation of realistic censored survival times is challenging. Most research studies use highly simplified models, such as the exponential, that do not adequately reflect the patterns of time to event and censoring seen in real datasets. In this article, I present a general method of simulating such data based on flexible parametric survival models (Royston and Parmar, 2002, Statistics in Medicine 21: 2175–2197). A key component of the approach is modeling not only the time to event but also the time to censoring. I illustrate the methods in data from clinical trials and from a prognostic study. I also describe a new Stata program, stsurvsim, that does the necessary calculations.