Structure searches of beryllium chalcogenides (BeS, BeSe, and BeTe) at high pressures using a swarm intelligence algorithm, in conjunction with density functional theory, reveal modulated polymorphs, unusual for such simple binary compounds. Apart from the well-known cubic (space group F-43m, zinc-blende structure) to hexagonal closed packed (space group P63/mmc, nickel-arsenide structure) structural transition, a further transition at higher pressure to an orthorhombic structure is predicted for BeS and BeSe. The orthorhombic phase is space group Cmca in BeS and Pnma before finally adopting Cmca in BeSe, each accompanied by the onset of modulation of the atomic arrangement. The amplitude of displacements associated with the modulation increases with increasing pressure and molecular dynamics simulations show the modulated structure to become stable at least to 300 GPa and 2000 K. This unusual structural modulation is not seen, however, in BeTe, which instead transforms to a C2/m phase. Links are drawn between the modulated phases of BeS and BeSe and the high-pressure modulated phases of their parent chalcogens. Our results provide key insights into understanding the modulation in binary compounds at high pressure.