The subject of this paper is the optimization of resource management in virtual distributed systems (VDS) via the application of machine learning algorithms, specifically Long Short-Term Memory (LSTM) networks. The aim is to develop an effective model for managing VDS using contemporary machine-learning techniques. Objectives are as follows: 1) to describe the problem of resource management challenges in VDS and the architecture of LSTM network.; 2) to collect and normalize historical data on resource usage, such as CPU, memory, disk, and network usage; 3) to develop a detailed architecture for the LSTM model, including input layers, multiple LSTM layers with dropout regularization, dense layers, and an output layer; 3) to train the LSTM model using TensorFlow and Keras, ensuring the training process includes at least 50 epochs, early stopping, and cross-validation techniques; 4) to evaluate the performance of the trained LSTM model using a test set, with MSE as the primary metric; 5) to conduct a thorough analysis of the training and validation outcomes, including the visualization of loss values over epochs. Methods involve designing an LSTM model to capture temporal dependencies and sequential patterns in resource usage data, including input layers, multiple LSTM layers with dropout regularization, dense layers, and an output layer. The normalized dataset was split into training and test sets, and the model was compiled using the Adam optimizer with a learning rate of 0.01 and mean squared error (MSE) as the loss function. The model was trained for 50 epochs with early stopping and cross-validation to prevent overfitting, and its performance was evaluated using MSE on a test set. The following results were obtained: 1) the historical data on resource usage, including CPU, memory, disk, and network usage; 2) the LSTM model demonstrated significant potential in managing VDS by efficiently analyzing and predicting optimal resource configurations; 2) visualization of the training process and revelations on how the model's loss values changed over epochs; 3) A comprehensive LSTM model architecture, including input layers, multiple LSTM layers with dropout regularization, dense layers, and an output layer. Conclusions. The primary contribution of this research is the development and training of LSTM models to optimize resource management in VDS using TensorFlow and Keras. This study presents a comprehensive methodology that includes collecting and normalizing historical resource usage data, designing the LSTM model architecture, training the model, and evaluating its performance. The results demonstrate the significant potential of LSTM models in effectively managing VDS by analyzing temporal dependencies and predicting optimal resource configurations. Specifically, the trained model achieved a mean squared error (MSE) below the target threshold, indicating robust predictive performance. The visualization of the training process revealed insights into overfitting and underfitting, with strategies like early stopping and cross-validation enhancing the model's generalizability. This study highlights the practical applicability of LSTM models, offering automated and optimized solutions for complex IT infrastructures, and laying the groundwork for future improvements in handling diverse and unforeseen data patterns in VDS.