AbstractGrouped survival data with possible interval censoring arise in a variety of settings. This paper presents nonparametric Bayes methods for the analysis of such data. The random cumulative hazard, common to every subject, is assumed to be a realization of a Lévy process. A time‐discrete beta process, introduced by Hjort, is considered for modeling the prior process. A sampling‐based Monte Carlo algorithm is used to find posterior estimates of several quantities of interest. The methodology presented here is used to check further modeling assumptions. Also, the methodology developed in this paper is illustrated with data for the times to cosmetic deterioration of breast‐cancer patients. An extension of the methodology is presented to deal with two interval‐censored times in tandem data (as with some AIDS incubation data).