Stacking sequence and, more generally, fibre orientation, are critical parameters in fibrous composite materials since they govern mechanical performance. This paper presents a method, based on the ultrasonic pulse-echo non-destructive technique, that can map the stacking sequence in unidirectional carbon-fibre composites. In-plane fibre orientation is measured using a Radon-transform method applied to local 2D images extracted from the 3D dataset formed from a 2D scan of pulse-echo responses. The ability to align these local 2D images to the plies in the region being assessed makes this technique suitable even in laminates where out-of-plane ply wrinkling is present. The Radon-transform method is shown to provide interpretable stacking-sequence maps, allowing ply lay-up sequence and both in-plane waviness and out-of-plane wrinkling to be visualised and quantified.