Reverberant Shear Wave Elastography (RSWE) is an ultrasound elastography technique that offers great advantages, however, current estimators generate underestimations and time-consuming issues. As well, the involvement of Deep Learning into the medical imaging field with new tools to assess complex problems, makes it a great candidate to serve as a new approach for a RSWE estimator. This work addresses the application of a Deep Neural Network (DNN) for the estimation of Shear Wave Speed (SWS) maps from particle velocity using numerically simulated data. The architecture of the proposed network is based on a U-Net, which works with a custom loss function specifically adopted for the reconstruction task. Four DNNs were trained using four different databases: clean, noisy, acquired at variable frequency, and noisy and acquired at variable frequency data. After the training of the DNNs, the predicted SWS maps were evaluated based on different metrics related to segmentation, regression and similarity of images. The model for clean data showed better results with a Mean Absolute Error (MAE) of 0.011, Mean Square Error(MSE) of 0.001, modified Intersection over Union (mIoU) of 98.4%, Peak Signal to Noise Ratio (PSNR) of 32.925 and a Structural Similarity Index Measure (SSIM) of 0.99, for 250 (size of Testing Sets); while the other models delivered SSIM in the range of 0.87 to 0.96. It was concluded that noisy and clean data could be effectively handled by the model, while the other ones still need enhancement. Clinical Relevance- This work is focused on the application of a Deep Learning approach to accurately asses the Shear Wave Speed in numerical simulations of Reverberant Shear Wave Elastography approach. This novel estimator could be useful for future clinical experiments specially with real time applications to determine the status of living tissue such as detection of malignant or benign tumors located in breast cervix prostate or skin and in the diagnosis of other pathologies such us liver fibrosis.