Modality corresponding to medical images is a vital filter in medical image retrieval systems. This article presents the classification of modalities of medical images based on the usage of principles of hyper-dimensional computing and reservoir computing. It is demonstrated that the highest classification accuracy of the proposed method is on a par with the best classical method for the given dataset (83% vs. 84%). The major positive property of the proposed method is that it does not require any optimization routine during the training phase and naturally allows for incremental learning upon the availability of new training data.