This chapter presents a short tutorial introduction to the theoretical investigations of two-dimensional inhomogeneous magnetic media. Simple examples are presented for the calculation of the spin-wave spectra of two-dimensional composite materials consisting of periodic square arrays of parallel cylinders made of a ferromagnetic material embedded in a ferromagnetic background. Each material is described by its spontaneous magnetization and exchange constant. An external static magnetic field is applied along the direction of the cylinders and both ferromagnetic materials are assumed to be magnetized parallel to this magnetic field. The spin-wave propagation in the plane perpendicular to the cylinders is considered. Gaps appear in the magnonic band structure of such composite systems. The existence of these gaps is investigated in relation to the physical parameters of the materials involved. The influence on the magnon band structure of the lattice parameter (distance between two cylinders) and the filling fraction of the cylinders are studied.