Multivariate survival data arises when subjects in the same group are related to each other or when there are multiple recurrences of the disease in the same subject. A common goal of survival analysis is to relate the outcome (time to event) to a set of covariates. In this paper, we focus on prognostic classification for multivariate survival data where identifying subgroups of patients with similar prognosis is of interest. We propose a computationally feasible method to identify prognostic groups with the widely used Classification and Regression Trees (CART) algorithm. The proposed method extends CART algorithm to multivariate survival data by introducing a gamma frailty to account for dependence among correlated events. The method is applied to a catheter infection data, and the performance of the method is also investigated by several simulation studies.