In earlier papers, Green [1–4], results have been presented which show the surface response of a cross-ply fiber composite plate due to buried impulsive sources. The sources considered were line loads and line double forces. The present paper extends these results for sources which are line couples and line double couples without moment. The impetus for carrying out this extensive study is the need for a thorough understanding of the nature of the stress waves generated as a result of internal impulsive events. This in turn is a prerequisite for the application of acoustic emission techniques which are now standard methods used for the detection of faults in engineering structures. This technique has the potential for not only locating the source of the emission but also for determining the nature of the source. The pulses arising from events such as crack formation, crack growth or the relative slip of crack surfaces are completely different in character and give rise to different signals at the receivers. By recording the time history of these signals it should be possible to determine the nature of the initiating event. This has particular relevance to the monitoring of laminated composites where there exists a wide variety of possible defects such as fiber breakage, matrix cracking, fiber/matrix debonding and ply delamination, in addition to the crack related events mentioned above. The surface response due to a number of different internal point sources in a plate of isotropic elastic material has been calculated by Ceranoglu and Pao [5] and by Vasudevan and Mal [6]. An analytical methodology for predicting the acoustic emission associated with crack propagation and arrest in an isotropic material has been developed by Jacobs et. al [7] and they have compared their theoretical predictions with experimental results. For fiber composite plates and laminates, Lih and Mal [8] have calculated the response of a unidirectional laminate to surface point loads and line loads, and the same authors [9] consider distributed surface loading on both cross-ply and quasi-isotropic plates. An experimental study of the relation between the received signals and the initiating events has been carried out by Ono and Huang [10].