The electronic structure and high pressure structural phase transition in lanthanum and cerium antimonides have been investigated using the tight binding LMTO method. Calculation of the total energy reveals that the simple tetragonal structure is stable at high pressure for both the compounds. In LaSb, the calculated values of the equilibrium cell volume and the cell volume at which phase transition occurs agree with the experimental results. However, in CeSb, the agreement is not so good. We have also predicted the most favouredc/a value in the simple tetragonal phase for these compounds. Further, we present the calculated results on the electronic structure of these systems at the equilibrium as well the reduced cell volumes.