The optical phonon modes and polaron properties in InSb at zero and under hydrostatic pressure are investigated using a pseudopotential approach. Our findings are compared to data in the literature, where possible, and found to be in reasonable agreement. The pressure dependence of longitudinal and transverse optical phonon frequencies, electron effective mass, Debye temperature of the longitudinal optical phonon frequency and polaron effective mass has been examined and discussed. All features of interest are found to vary monotonically upon compression. The results regarding polaron properties under pressure may be seen as the first predictions.