AbstractWe use high‐resolution capacitive dilatometry to study the low‐temperature linear magnetostriction of the bilayer ruthenate Sr3Ru2O7 as a function of magnetic field applied perpendicular to the ruthenium‐oxide planes ($B\parallel c$). The relative length change ${\rm \Delta }L(B)/L$ is detected either parallel or perpendicular to the c‐axis close to the metamagnetic region near B = 8 T. In both cases, clear peaks in the coefficient $\lambda (B) = {\rm d}({\rm \Delta }L/L)/{\rm d}B$ at three subsequent metamagnetic transitions are observed. For ${\rm \Delta }L \bot c$, the third transition at 8.1 T bifurcates at temperatures below 0.5 K. This is ascribed to the effect of an in‐plane uniaxial pressure of about 15 bar, unavoidable in the dilatometer, which breaks the original fourfold in‐plane symmetry.