Lg waves have the largest amplitudes in regional seismograms of the events within the continental crust. Lg waves are formed efficiently within the flat continental crust but their amplitudes reduce drastically while passing through regions with sudden crustal changes. For example it has been shown already that Lg waves are not passing through South Caspian Basin crust. To find why Lg wave blockage in South Caspian Basin, we have simulated Lg wave formation by finite difference numerical simulation of SH wave propagation in two dimensions. We solve SH wave equation using fourth order finite difference method. Our results show that the amplitude of the Lg waves of an event within the continental crust severely diminishes while passing through the South Caspian basin. We have also shown that for events happening within the oceanic-like South Caspian basin, no Lg waves forms neither within the basin nor outside of it.