Metazoan development proceeds through a series of morphogenetic events that sculpt body plans and organ structures. In the early embryonic stages, morphogenetic processes involving growth and deformation occur concurrently. Forces generated in one tissue can thus increase mechanical stress in the neighboring tissue, potentially disrupting spatial patterning, morphological robustness, and consequently decreasing organismal fitness. How organisms evolved mechanisms to reduce or release inter-tissue stresses remains poorly understood. Here we combined phylogenetic survey across a whole insect order (Diptera), quantitative live imaging, and functional mechanical perturbation to investigate the evolution of mechanical stress management during epithelial expansions in the gastrulating fly embryos. We find that two distinct cellular mechanisms exist in Diptera to prevent the accumulation of compressive stress that can arise when the expanding head and trunk tissues collide. In Cyclorrhapha, a monophyletic dipteran subgroup including the fruit fly Drosophila melanogaster, the head-trunk boundary undergoes active out-of-plane deformation to form a transient epithelial fold, called the cephalic furrow (CF), which acts as a mechanical sink to preempt head-trunk collision. Genetic or optogenetic elimination of the CF leads to tissue buckling, yielding deleterious effects of axial distortion that likely results from unmitigated release of compressive stress. Non-cyclorrhaphan flies, by contrast, lack CF formation and instead display widespread out-of-plane division in the head, which shortens the duration of its expansion and reduces surface area increase. Reorienting head mitosis in Drosophila from in-plane to out-of-plane partially suppresses the need for epithelial out-of-plane deformation, suggesting that out-of-plane division can act as an alternative mechanical sink to prevent tissue collision. Our data suggest that programs of mechanical stress management can emerge abruptly under selective pressure of inter-tissue mechanical conflict in early embryonic development.