The article is a follow-up to the Part 1: Experiments and analysis [1], in which a numerical model dealing with membrane structures supported by steel arches in software SOFiSTiK using 3D GNIA and 3D GNA is introduced and validated. This part investigates parametrically stability and buckling of arches of a barrel type membrane structure using linear buckling analysis (3D LBA). The in-plane and out of plane buckling factors of the arches for a vast spectrum of practical geometrical parameters of the structure, membrane pretension and support conditions of the arches and membrane frontiers are presented and confronted with the ones belonging to the arches alone.