A priori crystal structure prediction techniques have been used to explore the phase diagrams of hydrides ofmain group elements under pressure. Anumber of novel phases with the chemical formulas MHn, n > 1 and M = Li, Na, K, Rb, Cs; MHn, n > 2 and M= Mg, Ca, Sr, Ba; HnI with n > 1 and PH, PH2, PH3 have been predicted to be stable at pressures achievable in diamond anvil cells. The hydrogenic la...