Diagnosing lumbar discus hernia is a challenging task, due to disc and vertebral variations in size, shape, quantity, and appearance. Medical history and physical examination, electrodiagnostic tests, and MRIs are all used by doctors to set a definitive diagnosis. A majority of the state-of-the-art methods are semi-automatic and require extra corrections to the solution or are extremely sensitive to changes in parameters. Based on literature review, there is a solid basis for implementation of machine learning-based methods for disc herniation detection in MRI images. An automated segmentation method of vertebrae and discs is proposed in this study as a first step towards a decision support system for discus hernia identification. Dataset consisted of 104 images in sagittal and 99 images in axial views. Optimized convolutional neural network U-net has demonstrated very high accuracy in segmentation. Additional result represents the calculated distance from the disc's center to the disc's edge points in axial images across 360°, which results in clearly different number of peaks for the healthy and diseased discs. Fully automated computer diagnostic system helps speed up the process of setting up adequate diagnosis and reducing human mistakes.