In this paper, the structural, electronic and optical properties of LuPdBi and ScPdBi compounds are investigated using the density functional theory by WIEN2K package within the generalized gradient approximation, local density approximation, Engel–Vosco generalized gradient approximations and modified Becke–Johnson potential approaches. The topological phases and band orders of these compounds are studied. The effect of pressure on band inversion strength, electron density of states and the linear coefficient of the electronic specific heat of these compounds is investigated. Furthermore, the effect of pressure on real and imaginary parts of dielectric function, absorption and reflectivity coefficients of these compounds is studied.