External pressure loadings in sub-sea pipelines can generate catastrophic structural instabilities such as propagation buckling. This failure mode is typified by a pipe collapse (snap-through phenomenon) that occurs at an initiation pressure PIand a subsequent propagation of the collapse to pipe ends that occurs at a propagation pressure PP. Recent studies have shown that pipelines with a textured geometry, corresponding to the post-buckled shape of a thin-walled cylindrical pipe under axial compression, are able to substantially increase PI, PP, and thus resistance to propagation buckling, compared to conventional smooth pipelines. This study investigates the performance of alternative post-buckled shapes observed in thin-walled pipelines under hydrostatic loading. These shapes correspond closely to a geometric family known as curved-crease origami and so a geometric definition is developed to map geometric parameters from origami to pipelines. A numerical analysis is then conducted on two curved-crease forms and comparative smooth and textured forms. Textured and smooth numerical models show good correspondence with previously reported post-buckling behaviour. One curved crease form is shown to have an increase in PPthat is 10.8% greater than the textured pipeline and 131.8% greater than smooth.