This paper provides a practical stochastic method by which the maximum equilibrium scour depth around spherical bodies exposed to long-crested (2D) and short-crested (3D) nonlinear random waves can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves, and using the regular wave formulas for scour and self-burial depths by Truelsen et al. (2005). An example calculation is provided.