Manufactured parts containing composite materials can present challenging ultrasonic inspection problems. The inherent anisotropy of such materials acts to distort propagating ultrasonic beams, leading in turn to an associated distortion of defect images. Such distortions complicate the task of estimating the physical dimensions of a defect from its ultrasonic image. In the present work we demonstrate how these difficulties can be overcome by appropriately modelling the ultrasonic inspection process, and using the model to analyze defect images. To illustrate the approach, we consider a normal incidence through-transmission inspection of a flat uniaxial composite plate with an internal delamination. We begin by reviewing our model of the inspection process which incorporates the Gauss-Hermite model for beam propagation in anisotropic materials. The inspection model requires as inputs certain parameters which characterize the transducers, and others which characterize the composite material. We demonstrate how these parameters can be obtained from simple beam-mapping experiments. We then present experimental C-scan images of a seeded circular delamination in a composite plate, and compare these to images predicted by the model. Finally, we demonstrate how the model can be used to accurately size a delamination from its ultrasonic image.