Forward modeling of wave equations by Fourier transform is widely regarded for its high precision, small memory and moderate calculation time. In forward modeling, the stability problem must be considered. This paper derives a stability criterion for the simulation of elastic wave propagation by Fourier transform. The derived stability condition is v2k2△t2≤4, where v is the phase velocity, k is the wave number and △t is the time interval. Furthermore, stability is discussed for one-dimensional, two-dimensional and three-dimensional modeling respectively. For m-dimensional modeling by Fourier transform in elastic media, for a grid of cube, square or line segments where each side length of the grid is △d, then, when the modeling parameters satisfy vmax△t/△d≤2/(√mπ), the modeling process is stable.