An elasticity solution has been obtained for a long multilayered cylindrical shell of transversely isotropic layers subjected to axisymmetric radial load following Lekhnitskii-s stress function method. Numerical results are presented for a two layered shell for different ratios of thickness-to-outer radius and for different ratios of the moduli of elasticity in the radial direction of the layers. The results obtained from this analysis have been compared with those obtained from the multilayered shell theory of Ambartsumian.