The finite-difference technique is used to model Scholte wave propagation excited by a P-wave source in the water layer. The finite-difference approach encompasses models in which the parameters are allowed to vary with position both vertically and laterally, and is well suited for studies of the acoustic field at and below the seafloor. The finite-difference algorithm implemented is a 2-D acceleration-stress staggered grid scheme, of second order in time and order 2L in space. The formulation results in a simple numerical implementation of irregular liquid--solid interfaces. To investigate numerical issues which require special attention when implementing finite-difference schemes, the finite-different seismograms are compared with seismograms modeled by a fast-field technique valid for range-independent models. In particular, the methods are compared for models containing sharp liquid--solid interfaces representative of the seafloor. Numerical analysis indicates that the liquid--solid interface is located in a transition zone between fundamental finite-difference cells of constant parameters of liquid and solid. Excellent agreement with the transform technique is demonstrated.