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Extension to the cuspidal edges of wave surfaces in a plane of material symmetry of anisotropic solids is proposed via three different approaches. Two of the possible extensions stem from the definition of wave arrival used in the stationary phase approximation and the Cagniard-de Hoop technique for the calculation of the line source (2D) Green’s function. The third one is based on ray theory generalized to complex values of the group velocity. The stationary phase method yields an extension but only near to the cusp points. Concerning the two others methods, an extension for any angle of propagation can be obtained and it leads to a closed wave surface. The three methods are compared with experimental data and the extension given by the Cagniard technique best matches experimental measurements. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]