This work considers ultrasonic wave propagation in complex geometries and materials and the scattering of various types of flaws. Multi-Gaussian beam models are developed where the wave field of an ultrasonic transducer is simulated by the superposition of a few Gaussian beams. It is shown that the propagation and transmission/reflection of a Gaussian beam in both isotropic and anisotropic media with multiple curved interfaces can be compactly written in terms of A, B, C, D matrices that can then be multiplied together to determine the properties of the Gaussian beam. For anisotropic media, the Gaussian beam model is quite complex since it also depends on the slopes and curvatures of the slowness surface. It is demonstrated that this complexity can be considerably reduced through the use of slowness coordinates and that there is a new and efficient way to determine the slowness surface curvature terms. A number of simulation examples for both isotropic and anisotropic media demonstrate that multi-Gaussian beam models based on these formulations are both very versatile and efficient;Ultrasonic flaw scattering problems are solved in this work by use of the Kirchhoff and Born approximations. Through comparison with more exact scattering models it is shown that the Kirchhoff approximation for the pulse-echo response of both spherical voids and planar cracks in isotropic solids is valid over a much wider range of frequencies and angles normally assumed for this approximation provided the bandwidth of the ultrasonic system is sufficiently large. Using the Kirchhoff approximation a new analytical expression is obtained for the pulse-echo leading edge response of a volumetric flaw in a general anisotropic medium and for the response of an elliptical flat crack in a general anisotropic medium. The Born approximation has also been considered in this work. A new modified Born approximation is developed that substantially improves the ability of that approximation to predict the pulse-echo amplitude response of both strong and weak scattering inclusions in an isotropic solid. It is also shown that the form of this modified Born approximation remains valid for anisotropic media as well.