Phased array ultrasonic testing is widely used to test structures for flaws due to its ability to produce steered and focused beams. The inherent anisotropic nature of some materials, however, leads to skewing and distortion of the phased array beam and consequently measurement errors. To overcome this, a quantitative model of phased array beam propagation in such materials is required, so as to accurately model the skew and the distortion. The existing phased array beam models which are based on exact methods or numerical methods are computationally expensive or time consuming. This article proposes a modeling approach based on developing the linear phased multi-Gaussian beam (MGB) approach to model beam steering in anisotropic media. MGBs have the advantages of being computationally inexpensive and remaining non-singular. This article provides a comparison of the beam propagation modeled by the developed ordinary Gaussian beam and linear phased Gaussian beam models through transversely isotropic austenitic steel for different steering angles. It is shown that the linear phased Gaussian beam model outperforms the ordinary one, especially at steering angles higher than 20° in anisotropic solids. The proposed model allows us to model the beam propagation from phased arrays in both isotropic and anisotropic media in a way that is computationally inexpensive. As a further step, the developed model has been validated against a finite element model (FEM) computed using COMSOL Multiphysics.@en