Shells of revolution under axisymmetric conditions exhibit a circumferentially uniform pre-buckling stress state and are important fundamental systems which often serve as reference systems for those under more complex conditions. Given this status, work is continuing on a careful and complete characterization of their buckling response with the aid of the Reference Resistance Design (RRD) framework for the ultimate benefit of the EN 1993-1-6 Eurocode on the strength of stability of metal shells. The situation is greatly complicated by the fact that while modern finite element software packages offer axisymmetric shell elements in an efficient 2D modelling plane, these are not capable of detecting bifurcation buckling into non-axisymmetric modes which are often critical for slender systems. Reverting to a full 3D plane is possible, but grossly inefficient and the explicitly modelled circumferential direction is parasitic and detrimental to the overall solution quality. AQUINAS is an accessible and intuitive toolbox developed by the Authors in MATLAB for the efficient analysis of axisymmetric shell structures, aiming to reintroduce a modelling capability that was once standard in the field. Data input is entirely object-oriented and matrix assembly is parallelized with pre-compiled C++ routines, with users being able to take direct advantage of MATLAB's visualization properties. The software natively supports the LA, LBA, MNA, GMNIA etc. Eurocode analysis taxonomy. This paper demonstrates the current capabilities of the toolbox, describes the extensive programme of verification against existing established solutions that has been performed, and illustrates its ability to efficiently compute very detailed capacity curves using the EN 1993-1-6 capacity curve framework.