The influence of hydrostatic pressure on structural, electronic and optical properties of short period (BeS)(1)/(BeSe)(1), (BeSe)(1)/(BeTe)(1) and (BeS)(1)/(BeTe)1 superlattices, has been investigated. The lattice parameters a and c for the tetragonal unit cell obtained by total energy calculations are in good agreement with the values calculated by macroscopic elasticity theory. The (BeS)(1)/(BeSe)(1) superlattice possesses an indirect band gap while (BeSe)(1)/(BeTe)(1) and (BeS)(1)/(BeTe)(1) superlattices possess a direct band gap. The pressure ranges from 0 to 47 GPa for (BeS)(1)/(BeSe)(1), 0 to 39 GPa for (BeSe)(1)/(BeTe)(1), and 0 to 45 GPa for (BeS)(1)/(BeTe)(1) , meanwhile the pressure dependence of the energy band gap along different symmetry directions obey the equation E-g(p)= E-g+ ap + bp(2). The pressure coefficient of the indirect band gap for (BeS)(1)/(BeSe)(1) is - 22.5675 x 10(-3) eV(GPa)(-1), while that of the direct band gap is estimated as - 25.8581 x 10(-3)eV(GPa)(-1) and - 24.4695 x 10(-3)eV(GPa)(-1) for (BeSe)(1)/(BeTe)(1) and (BeS)(1)/(BeTe)(1), respectively. The variation of the static dielectric constant with pressure is discussed.