Computer simulations of magnetic domain structure in thin films of amorphous rare-earth transition metal magneto-optic recording media are performed. In these simulations, the recording media are two-dimensional lattice of 64 x 64 magnetic moments with a lattice distance of 10 Angstrom. The motion of the magnetic moments follows the dynamic Landau-Lifshitz-Gilbert (LLG) equation under the influence of an effective field arising from the local anisotropy, nearnest-neighbor exchange, classical dipole-dipole interaction, and an external applied field. Within the constraints of the LLG equation, we have investigated the process of domain wall formation for a medium with random anisotropy orientation. Even for very small randomness of anisotropy orientation, it is found that the 2 pi-Bloch wall line appears at the boundaries of magnetic domains and the domain wall is jagged. Finally, the effects of exchange stiffness coefficient A, and anisotropy coefficient K-u on the wall width and the jaggedness which measured the straightness of domain wall are studied. (C) 1996 American Institute of Physics.