Carbon Capture and Storage (CCS) field is growing rapidly as a means to mitigate the accumulation of greenhouse gas emissions. However, the geomechanical stability of CCS systems, particularly related to bearing capacity, remains a critical challenge that requires accurate prediction models. In this research paper, we investigate the efficacy of employing an Autoregressive Deep Neural Network (ARDNN) algorithm to predict the geomechanical bearing capacity in CCS systems through shear wave velocity prediction as an index for bearing capacity evaluation of deep rock formations. The model utilizes a dataset consisting of 23,000 data points to train and test the ARDNN algorithm. Its scalability, use of deep learning techniques, automatic feature extraction, adaptability to changes in data, and versatility in various prediction tasks make it an attractive option for accurate predictions. The results demonstrate exceptional performance, as evidenced by an R-squared value of 0.9906 and a mean squared error of 0.0438 for the test data compared to the measured data. This research has significant practical implications for effectively predicting geomechanical stability in CCS systems, thus mitigating potential risks associated with their operation.