The Earth's core is expected to contain around 10 wt % light elements (S, Si, O, possibly C, H, etc.) alloyed with Fe and Ni. Very little is known about these alloys at pressures and temperatures of the core. Here, using the evolutionary crystal structure prediction methodology, we investigate Fe-Si compounds at pressures of up to 400 GPa, i.e. covering the pressure range of the Earth's core. Evolutionary simulations correctly find that at atmospheric pressure the known non-trivial structure with P213 symmetry is stable, while at pressures above 20 GPa the CsCl-type structure is stable. We show that among the possible Fe silicides (Fe3Si, Fe2Si, Fe5Si3, FeSi, FeSi2 and FeSi3) only FeSi with CsCltype structure is thermodynamically stable at core pressures, while the other silicides are unstable to decomposition into Fe + FeSi or FeSi + Si. This is consistent with previous works and suggests that Si impurities contribute to stabilization of the body-centered cubic phase of Fe in the inner core.