Introduction: The implementation of data storage process requires timely scaling of the infrastructure to accommodate the data received for storage. Given the rapid accumulation of data, new models of storage capacity management are needed, which should take into account the hierarchical structure of the data storage, various requirements for file storage and restrictions on the storage media size. Purpose: To propose a model for timely scaling of the storage infrastructure based on predictive estimates of the moment when the data storage media is fully filled. Results: A model of storage capacity management is presented, based on the analysis of storage system state patterns. A pattern is a matrix each cell of which reflects the filling state of the storage medium at an appropriate level in the hierarchical structure of the storage system. A matrix cell is characterized by the real, limit, and maximum values of its carrier capacity. To solve the scaling problem for a data storage system means to predict the moments when the limit capacity and maximum capacity of the data carrier are reached. The difference between the predictive estimatesis the time which the administrator has to connect extra media. It is proposed to calculate the values of the predictive estimates programmatically, using machine learning methods. It is shown that when making a short-term prediction, machine learning methods have lower accuracy than ARIMA, an integrated model of autoregression and moving average. However, when making a long-term forecast, machine learning methods provide results commensurate with those from ARIMA. Practical relevance: The proposed model is necessary for timely allocation of storage capacity for incoming data. The implementation of this model at the storage input allows you to automate the process of connecting media, which helps prevent the loss of data entering the system.