Understanding how forces orchestrate tissue formation requires technologies to map internal tissue stress at cellular length scales. Here, we develop ultrasoft mechanosensors that visibly deform under less than 10 Pascals of cell-generated stress. By incorporating these mechanosensors into multicellular spheroids, we capture the patterns of internal stress that arise during spheroid formation. We experimentally demonstrate the spontaneous generation of a tensional 'skin', only a few cell layers thick, at the spheroid surface, which correlates with activation of mechanobiological signalling pathways, and balances a compressive stress profile within the tissue. These stresses develop through cell-driven mechanical compaction at the tissue periphery, and suggest that the tissue formation process plays a critically important role in specifying mechanobiological function. The broad applicability of this technique should ultimately provide a quantitative basis to design tissues that leverage the mechanical activity of constituent cells to evolve towards a desired form and function.