Survival analysis revolves around studying and predicting the time it takes for a particular event to occur. In clinical trials on terminal illnesses, this is usually the time from the diagnosis of a patient until their death. Estimating the odds of survival of a new patient can be done by analyzing survival data from past patients in similar conditions. To cluster similar patients based on a set of features, survival trees may be employed, which act as decision trees that assign a survival distribution to each cluster. Many algorithms exist for creating useful survival trees, but not for creating optimal survival trees. In this paper, research on finding optimal classification trees is applied to survival analysis, by adapting the MurTree algorithm to construct survival trees. We present SurTree, an algorithm that applies many of MurTree’s techniques to create globally optimal survival trees. Furthermore, we compare the output quality and runtime performance of SurTree to a state-of-the-art method for constructing survival trees, showing its optimality and its fast computation times on smaller datasets.