The problem of calculating the possible free oscillations in its plane of an infinitesimally thin disk of self-gravitating material is posed as an eigen value problem involving infinite matrices. This problem has a simpler form when axisymmetric modes only are considered. An analytical solution is not in general possible, though one exists for the particular case of a uniformly rotating disk. Numerical calculations of axisymmetric modes of oscillation of a number of disk models are presented, one of which is derived from fitting observational data for M 31. The more difficult problem of calculating non-axisymmetric modes of oscillation is also considered.