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Quantifying segmentation uncertainty has become an important issue in medical image analysis due to the inherent ambiguity of anatomical structures and its pathologies. Recently, neural network-based uncertainty quantification methods have been successfully applied to various problems. One of the main limitations of the existing techniques is the high memory requirement during training; which limits their application to processing smaller field-of-views (FOVs) and/or using shallower architectures. In this paper, we investigate the effect of using reversible blocks for building memory-efficient neural network architectures for quantification of segmentation uncertainty. The reversible architecture achieves memory saving by exactly computing the activations from the outputs of the subsequent layers during backpropagation instead of storing the activations for each layer. We incorporate the reversible blocks into a recently proposed architecture called PHiSeg that is developed for uncertainty quantification in medical image segmentation. The reversible architecture, RevPHiSeg, allows training neural networks for quantifying segmentation uncertainty on GPUs with limited memory and processing larger FOVs. We perform experiments on the LIDC-IDRI dataset and an in-house prostate dataset, and present comparisons with PHiSeg. The results demonstrate that RevPHiSeg consumes ~30% less memory compared to PHiSeg while achieving very similar segmentation accuracy.