Background and Objective: Accurate and reliable segmentation of the prostate gland in MR images can support the clinical assessment of prostate cancer, as well as the planning and monitoring of focal and loco-regional therapeutic interventions. Despite the availability of multi-planar MR scans due to standardized protocols, the majority of segmentation approaches presented in the literature consider the axial scans only. In this work, we investigate whether a neural network processing anisotropic multi-planar images could work in the context of a semantic segmentation task, and if so, how this additional information would improve the segmentation quality. Methods: We propose an anisotropic 3D multi-stream CNN architecture, which processes additional scan directions to produce a high-resolution isotropic prostate segmentation. We investigate two variants of our architecture, which work on two (dual-plane) and three (triple-plane) image orientations, respectively. The influence of additional information used by these models is evaluated by comparing them with a single-plane baseline processing only axial images. To realize a fair comparison, we employ a hyperparameter optimization strategy to select optimal configurations for the individual approaches. Results: Training and evaluation on two datasets spanning multiple sites show statistical significant improvement over the plain axial segmentation (on the Dice similarity coefficient). The improvement can be observed especially at the base (0.898 single-plane vs. 0.906 triple-plane) and apex (0.888 single-plane vs. 0.901 dual-plane). Conclusion: This study indicates that models employing two or three scan directions are superior to plain axial segmentation. The knowledge of precise boundaries of the prostate is crucial for the conservation of risk structures. Thus, the proposed models have the potential to improve the outcome of prostate cancer diagnosis and therapies.