In this thesis, the magnetic reversal of a Permalloy disk at the nano-scale has been investigated by means of OOMMF software, which employs the finite difference (FD) method to solve Landau-Lifshitz-Gilbert (LLG) equation. The magnetic nanodot configurations depends significantly on both dot diameter and thickness. Depending on the disk size , many (meta)stable magnetic patterns such as vortex, and various buckling states are observed. The results Suggest that the disk size is the decisive factor in determining which states is more favorable than the others, and particularly the disk diameter determines whether some in-plane buckling can be sustainable. We also concluded that there is a distinct behavior switch between the vortex state and the single-domain state, depending on the diameter of the nanomagnet.