A collapsible product has a tubular body of resilient material, the tubular body having an outer surface and an inner surface, a length, a wall between the outer surface and the inner surface, and a longitudinal axis. The tubular body wall is split longitudinally along its length, at a first perimeter location on the tube. The tubular body wall is also cut longitudinally along its length, partially through its wall thickness from the inner surface, at one or more inner perimeter locations. The tubular body wall is further cut longitudinally along its length, partially through its wall thickness from the outer surface, at two or more outer perimeter locations. The longitudinal cuts enable a controlled collapse of the tubular body, which can be efficiently packaged for shipping. The collapsible product may be tubular fiberglass pipe insulation, or another kind of product.