The ability to predict hidden phases under extreme conditions is not only crucial to understanding and manipulating materials but it could also lead to insight into new phenomena and novel routes to synthesize new phases. This is especially true for Ruddlesden-Popper perovskite phases that possess interesting properties ranging from superconductivity and colossal magnetoresistance to photovoltaic and catalytic activities. In particular, the physical properties of the bilayer perovskite Sr3Ru2O7 at the surface are intimately tied to the rotation and tilt of the RuO6 octahedra. To take advantage of the extra degree of freedom associated with tilting we have performed first principles hybrid density functional simulations of uniaxial pressure applied along the c-axis of bulk Sr3Ru2O7 where we find that the octahedra become tilted, leading to two phase transitions. One is a structural transition at [Formula: see text]1.5 GPa, and the other is from a ferromagnetic (FM) metal to an antiferromagnetic (AFM) insulator at [Formula: see text]21 GPa whose AFM spin configuration is different from the AFM state near the FM ground state.