The prediction of open stope hangingwall (HW) stability is a crucial task for underground mines. In this paper, a relatively novel technique, the random forest (RF) algorithm, is introduced for the prediction of HW stability. The objective of this study is to verify the feasibility of the RF algorithm on HW stability prediction and investigate the relative importance of influencing variables. The training and verification of RF models were conducted on a dataset from the literature and a total of 115 HW cases were analysed. Thirteen influencing variables were selected as the inputs with the HW stability being selected as the output. The dataset was randomly divided into the training set and the testing set. Fivefold cross-validation was used as the validation method, and the grid search method was used for the hyper-parameters tuning. Performance measures were chosen to be the confusion matrix, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC). The results show that the RF algorithm had great potential for the prediction of HW stability. AUC values achieved by the optimum RF model on the training set and the testing set were 0.884 and 0.873, respectively, indicating that the optimum RF model was excellent at predicting HW stability. The stope design method was found to be the most sensitive variable among all variables evaluated, with an importance score of 0.168 out of 1. The RQD and HW height also had a strong influence on the stability of an open stope HW.