Structural applications of thin shells rely on their ability to equilibrate loads through efficient membrane action rather than bending, which translates into low-cost and low-weight optimised designs. However, thin shells of revolution are very sensitive to buckling failures: their rich and complex stability behaviour has been the focus of extensive research and led to the development of increasingly advanced analytical and computational tools from the middle of the 20th century. Modern design approaches offer simplified methods for safe design in some cases, but structures such as multi-segment shells of revolution require non-trivial calculations at every step of the way, from a linear elastic stress analysis to a fully nonlinear buckling analysis. Although powerful computational tools exist to conduct these, they require expert knowledge to obtain significative results, even at the level of a linear elastic stress analysis, and are generally not easily accessible. This research aims to facilitate the safe design of multi-segment thin shells of revolution by proposing tools specialised for their analysis that would be more accessible than those currently publicly available. Within the context of Finite Element analysis, specialised shape functions are derived from the governing differential equations to accurately capture boundary layer bending without need for local mesh refinement. This approach is successfully applied to the linear elastic stress analysis of thin shells under axisymmetric condition, leading to the definition of the Cylindrical Shell Boundary Layer (CSBL) and Conical Shell Boundary Layer (CoSBL) elements. The former is extended to treat non-axisymmetric problems through a Fourier decomposition approach. A novel treatment of Linear Bifurcation Analysis with axisymmetric pre-buckling conditions that exploits the interpolation capabilities of the parametric bending shape functions of the Fourier CSBL is implemented and tested. The validity of the proposed approach for linear analysis was confirmed, and benchmark results from a first implementation of the LBA method show potential for the method to become a convenient and efficient tool for multi-segment shells of revolution design.