An integral transform method is employed to predict the normal surface displacement resulting from the elastic waves initiated by a variety of line sources embedded within plates and laminates. Results are derived for a monolithic isotropic plate, a symmetric isotropic laminate consisting of an inner core of one elastic material sandwiched between two outer layers of a different elastic material, and an anisotropic laminate formed of four layers of a fibre composite material. The sources consist of line couples and line double forces, located at a quarter the overall laminate depth below the surface. Receiver signals are simulated at distances of two, four and ten plate depths from the plane of action of the source. The results bring out the effects of reflections from the internal interfaces as well as from the traction free bounding surfaces of the laminates.