This paper establishes the three-dimensional elasticity solution for infinitely long, arbitrarily laminated, anisotropic cylindrical panels with simply supported boundary condition under transverse loading. Using a series method, the solution can be formulated exactly. In this study, three groups of stacking sequences with unsymmetric, antisymmetric, and symmetric laminations are used to investigate the behavior of cylindrical panels. They are laminates with [<(theta)over bar>degrees/90 degrees], [<(theta)over bar>degrees/-<(theta)over bar>degrees], and [<(theta)over bar>degrees/-<(theta)over bar>degrees/<(theta)over bar><degrees]. The results shown in this paper include deflections, inplane stresses, and transverse stresses. From the present study, it is found that the deflection is controlled by the ply with fiber direction perpendicular to the axis of the panel. The in-plane stresses are basically linear through the thickness. The distributions of transverse normal stresses dominated by the curvature of the shell is quite different from those of laminated plates. The initial curvature effect is again found to be very important.