Multi-parametric MR images have been shown to be effective in the non-invasive diagnosis of prostate cancer. Automated segmentation of the prostate eliminates the need for manual annotation by a radiologist which is time consuming. This improves efficiency in the extraction of imaging features for the characterization of prostate tissues. In this work, we propose a fully automated cascaded deep learning architecture with residual blocks (Cascaded MRes-UNET) for segmentation of the prostate gland and the peripheral zone in one pass through the network. The network yields high dice scores (mean=0.91) with manual annotations from an experienced radiologist. The average difference in volume estimation is around 6% in the prostate and 3% in the peripheral zone.