This article concerns robust modeling of the survival time for cancer patients. Accurate prediction of patient survival time is crucial to the development of effective therapeutic strategies. To this goal, we propose a unified Expectation‐Maximization approach combined with theL1‐norm penalty to perform variable selection and parameter estimation simultaneously in the accelerated failure time model with right‐censored survival data of moderate sizes. Our approach accommodates general loss functions, and reduces to the well‐known Buckley‐James method when the squared‐error loss is used without regularization. To mitigate the effects of outliers and heavy‐tailed noise in real applications, we recommend the use of robust loss functions under the general framework. Furthermore, our approach can be extended to incorporate group structure among covariates. We conduct extensive simulation studies to assess the performance of the proposed methods with different loss functions and apply them to an ovarian carcinoma study as an illustration.