We rigorously derive the von Karman shell theory (and the resulting von Karman equations) for incompressible materials. Our approach is variational and starts from the general nonlinear 3-dimensional elastic energy functional. Our only assumption is that the midsurface of the shell enjoys the following approximation property: C3 first order infinitesimal isometries are dense in the space of all W^{2, 2} infinitesimal isometries. The class of surfaces with this property includes: flat surfaces, convex surfaces, developable surfaces and rotationally invariant surfaces.