We discuss the development of a high accuracy and low computational complexity global stability solver for bluff body geometries based on Chebyshev Spectral collocation method. We propose and validate a series of co-ordinate transformations for the generation of a Chebyshev spectral collocated orthogonal grid from the body-conformed grid of bluff body geometries. The inverse Karman-Trefftz and the Joukowsky transformations are used in conjunction with algebraic transformations to transform the body-conformed grid of circular cylinders and airfoils into the orthogonal grid. The global stability equation is solved as an Eigen Value problem on the Chebyshev spectral collocated grid obtained after the transformations. The solver was validated by analysing the stability of the Blasius profile at Reynolds number (based on displacement thickness), $𝑅𝑒_{𝛿^∗}$=580 and wave number, 𝛼=0.179 to successfully reproduce the local stability results. The validation of the technique was done by analysing stability of circular cylinders, symmetric and cambered airfoils in addition to square cylinder and wedge flows and will be presented at the time of conference.