The stress analysis of functionally graded thick hollow cylindrical and spherical pressure vessels under the effect of uniform magnetic field are examined. These pressure vessels are designed in such a way that the material properties and magnetic permeability are exponentially graded in radial direction, provided that the inner surface is pure metal and the outer surface is pure ceramic. The differential equations with variable coefficients obtained under these conditions are handled by both Complementary Functions Method and Pseudospectral Chebyshev Method. Benchmark solutions available in the literature for some special cases are used to confirm the results. The effects of different mixture and uniform magnetic field on stresses and displacement distribution are shown in graphical form.