The question of what guides lineage segregation is central to development, where cellular differentiation leads to segregated cell populations destined for specialized functions. Here, using optical tweezers measurements of mouse embryonic stem cells (mESCs), we reveal a mechanical mechanism based on differential elasticity in the second lineage segregation of the embryonic inner cell mass into epiblast (EPI) cells - that will develop into the fetus - and primitive endoderm (PrE) - which will form extraembryonic structures such as the yolk sac. Remarkably, we find that these mechanical differences already occur during priming and not just after a cell has committed to differentiation. Specifically, we show that the mESCs are highly elastic compared to any other reported cell type and that the PrE cells are significantly more elastic than EPI-primed cells. Using a model of two cell types differing only in elasticity we show that differential elasticity alone can lead to segregation between cell types, suggesting that the mechanical attributes of the cells contribute to the segregation process. Our findings present differential elasticity as a previously unknown mechanical contributor to the lineage segregation during the embryo morphogenesis.