Localized structures in anharmonic lattice systems called intrinsic localized modes (ILMs) are investigated numerically. ILMs are time-periodic and spatial-localized structures due to nonlinearity and discreteness of anharmonic lattices systems. We find that two types of ILMs exist in two dimensional square lattice systems in terms of structures: quasi-one dimensional ILMs and two dimensional ones. Adding to this, we find ILMs envelope and internal frequency are highly depend on lattice structures and interaction potential. We also show that quasi-one dimensional ILMs can move with keeping their localized structures.