The pressure dependence of exciton properties, optical phonon modes, polaron characteristics and plasma frequency of GaSb has been investigated using a pseudopotential approach combined with Harrison and Adachi's models. The obtained results show reasonable accord with data available in the literature. The enhanced pressure from 0 to 40 kbar increases the exciton reduced mass monotonously and in a non-linear way. The screening effect makes the Bohr radius much larger than the lattice parameter of these semiconductor materials. The phonon frequency modes increase with increasing pressure. This is due to the pressure effect that brought atoms closer to each other and thus they sit in steeper potential wells. The Fröhlich coupling constant decreases monotonously with increasing pressure. This reflects the reduction of the lattice asymmetrical local deformation when GaSb is subjected to pressure. The applied pressure makes the plasma system of GaSb creates longer wavelengths which give ions a large amount of kinetic energy. The information obtained from this contribution may become good guidance for use of the material in question in several device applications, e.g., in infrared optical sources and thermo photovoltaic systems.