Different modes of instability might occur in thin-walled stiffened shells. In particular, local shell and stringer buckling modes and global buckling mode might develop in axially stiffened cones. In this paper, such modes are studied in conical shells under axial compression through a linear eigenvalue finite element analysis. In order to examine buckling modes in isolation (in line with typical simplified formulae) as well as competing modes together, use is made of different finite element models, including discrete and smeared models. Changes of buckling modes are captured by varying stiffener slenderness, number of stiffeners and tapering angle, treated as design parameters. Some evidence of mode interaction is recorded by the clustering of eigenvalues/eigenmodes.