Results are presented from numerical simulations of the incidence of a spatially-compact beam of internal waves on a shear layer containing a critical level. It is found that a significant fraction of the energy of the incident beam is transmitted across the critical level when the packet is narrow in physical space and when the energy density of the packet is not too high so that nonlinear effects are weak. As either the packet width or its energy density increases, the presence of a critical level renders the shear layer increasingly opaque to the transmission of energy. The familiar exponentially small value of the transmission coefficient is recovered as the spatial width of the packet exceeds (roughly) eight to ten wave lengths.