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Breast tumor segmentation is one of the key steps that helps us characterize and localize tumor regions. However, variable tumor morphology, blurred boundary, and similar intensity distributions bring challenges for accurate segmentation of breast tumors. Recently, many U-net variants have been proposed and widely used for breast tumors segmentation. However, these architectures suffer from two limitations: (1) Ignoring the characterize ability of the benchmark networks, and (2) Introducing extra complex operations increases the difficulty of understanding and reproducing the network. To alleviate these challenges, this paper proposes a simple yet powerful nested U-net (NU-net) for accurate segmentation of breast tumors. The key idea is to utilize U-Nets with different depths and shared weights to achieve robust characterization of breast tumors. NU-net mainly has the following advantages: (1) Improving network adaptability and robustness to breast tumors with different scales, (2) This method is easy to reproduce and execute, and (3) The extra operations increase network parameters without significantly increasing computational cost. Extensive experimental results with twelve state-of-the-art segmentation methods on three public breast ultrasound datasets demonstrate that NU-net has more competitive segmentation performance on breast tumors. Furthermore, the robustness of NU-net is further illustrated on the segmentation of renal ultrasound images. The source code is publicly available on https://github.com/CGPzy/NU-net.