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Quantitative studies of embryogenesis require the ability to monitor pattern formation and morphogenesis in large numbers of embryos, at multiple time points and in diverse genetic backgrounds. We describe a simple approach that greatly facilitates these tasks for Drosophila melanogaster embryos, one of the most advanced models of developmental genetics. Based on passive hydrodynamics, we developed a microfluidic embryo-trap array that can be used to rapidly order and vertically orient hundreds of embryos. We describe the physical principles of the design and used this platform to quantitatively analyze multiple morphogen gradients in the dorsoventral patterning system. Our approach can also be used for live imaging and, with slight modifications, could be adapted for studies of pattern formation and morphogenesis in other model organisms.