Breast augmentation is one of the most frequently performed cosmetic procedures worldwide, but it carries certain risks including breast implant rupture. Timely and accurate diagnostics of ruptures are crucial, as undiagnosed ruptures can lead to serious health complications. Imaging methods, such as magnetic resonance imaging (MRI), are recommended for the diagnosis of breast implants due to their high accuracy. However, current diagnostics rely heavily on the subjective interpretation and experience of the physician. This study investigates the potential of neural networks (NN) to address this limitation and improve the accuracy of rupture detection in silicone breast implants. We applied a deep learning-based neural network system trained on MRI images of breast implants to detect ruptures. The dataset included annotated MRI scans of symptomatic and asymptomatic patients with confirmed implant integrity or rupture. Several models were trained using ResNet-18, ResNet-50, and Xception networks, with various hyperparameter settings and augmentation techniques applied to enhance model performance and generalizability. The performance of the NN model was evaluated using confusion matrices and standard metrics such as true positive rate (TPR) and true negative rate (TNR). A semi-automated algorithm for the detection of intracapsular ruptures of breast implants on MRI was successfully developed. The algorithm correctly detected ruptures in 95.4% of cases and accurately identified cases without rupture in 86.7% of instances. Our findings highlight the potential of neural networks as a supportive tool in diagnosing breast implant ruptures. By semi-automating rupture detection, NNs can reduce diagnostic errors, expedite image evaluation, and optimize resource use in medical practice. The study underscores the importance of combining artificial intelligence with expert evaluation to enhance patient care and reduce costs in medical diagnostics.