This presentation reports on the extension of an established CNDE ultrasound beam transmission model to accommodate transmission in generally anisotropic materials. Using principles of elastodynamic reciprocity, the model expresses the internal wave field as a surface integral over the radiating transducer, employing the full Green function (point force response function) for the combined body under inspection and the coupling medium. The model evaluates the Green function asymptotically for short wavelength, and is therefore referred to as an asymptotic Green function model (AGF). The integrand of the transducer integral is projected on to a discretely orthogonal Gaussian basis, leading to a fully analytical evaluation. Extension of the model to accommodate generally anisotropic materials requires asymptotic analysis of the full Green function for an elastically anisotropic body. The approach taken to numerical implementation of this asymptotic evaluation will be summarized, and examples of application to beam transmission in single crystal metals and CFRP composites will be presented. Plans for incorporating the transmission model into CNDE UTSIM ultrasound inspection simulation software will be summarized.