AbstractWe propose to combine the benefits of flexible parametric survival modeling and regularization to improve risk prediction modeling in the context of time‐to‐event data. Thereto, we introduce ridge, lasso, elastic net, and group lasso penalties for both log hazard and log cumulative hazard models. The log (cumulative) hazard in these models is represented by a flexible function of time that may depend on the covariates (i.e., covariate effects may be time‐varying). We show that the optimization problem for the proposed models can be formulated as a convex optimization problem and provide a user‐friendly R implementation for model fitting and penalty parameter selection based on cross‐validation. Simulation study results show the advantage of regularization in terms of increased out‐of‐sample prediction accuracy and improved calibration and discrimination of predicted survival probabilities, especially when sample size was relatively small with respect to model complexity. An applied example illustrates the proposed methods. In summary, our work provides both a foundation for and an easily accessible implementation of regularized parametric survival modeling and suggests that it improves out‐of‐sample prediction performance.