The effect of pressure on the structural and electronic properties of the two binary compounds SrSe and SrTe have been investigated in the present work. The calculations were carried out with the CASTEP code which uses the density functional theory (DFT) based on the pseudopotential and plane-wave (PW-PP) method. To evaluate the exchange and correlation energy, we used the generalized gradient approximation (GGA-PBE). Our results show that, at ambient conditions, the two studied compounds are more stable in the NaCl-type phase (B1). Under the effect of pressure, the two materials undergo a phase transition to crystallize in the CsCl-like structure (B2) at pressures equal to 16 GPa and 12.33 GPa for the compounds SrSe and SrTe, respectively. Analysis of the band structure under conditions of pressure and zero temperature shows that the two compounds are indirect semiconductors. Under the effect of pressure, our calculations predict that the two compounds change electronically to become metals at pressures greater than 46 GPa for SrSe and 13 GPa for SrTe. To give a quantitative description of the variation of the structural and electronic parameters of the two structures with the pressure, we extracted the parametric functions of these parameters as a function of the pressure. Our results are presented and compared with a different experimental and theoretical works.