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B-mode ultrasound is commonly used to image musculoskeletal tissues, but one major bottleneck is data interpretation, and analyses of muscle thickness, pennation angle and fascicle length are often still performed manually. In this study we trained deep neural networks (based on U-net) to detect muscle fascicles and aponeuroses using a set of labelled musculoskeletal ultrasound images. We then compared neural network predictions on new, unseen images to those obtained via manual analysis and two existing semi/automated analysis approaches (SMA and Ultratrack). With a GPU, inference time for a single image with the new approach was around 0.7s, compared to 4.6s with a CPU. Our method detects the locations of the superficial and deep aponeuroses, as well as multiple fascicle fragments per image. For single images, the method gave similar results to those produced by a non-trainable automated method (SMA; mean difference in fascicle length: 1.1 mm) or human manual analysis (mean difference: 2.1 mm). Between-method differences in pennation angle were within 1$^\circ$, and mean differences in muscle thickness were less than 0.2 mm. Similarly, for videos, there was strong overlap between the results produced with Ultratrack and our method, with a mean ICC of 0.73, despite the fact that the analysed trials included hundreds of frames. Our method is fully automated and open source, and can estimate fascicle length, pennation angle and muscle thickness from single images or videos, as well as from multiple superficial muscles. We also provide all necessary code and training data for custom model development.