The focus of this work is on the development of asymptotically-accurate nonlinear hyperelastic constitutive model for thin shell structures using Variational Asymptotic Method (VAM). In this work, these structures are analyzed for both geometric and material nonlinearities. The geometric nonlinearity is handled by allowing finite deformations and generalized warping functions through Green strain, while the material nonlinearity is incorporated through strain energy density function of hyperelastic material model. Using the inherent small parameters (moderate strains, very small thickness-to-wavelength ratio and very small thickness-to-initial radius of curvature) for the application of VAM, the process begins with three-dimensional nonlinear hyperelasticity and it weakly decouples the analysis into a one-dimensional through-the-thickness nonlinear analysis and a two-dimensional nonlinear shell analysis. Through-the-thickness analysis is analytical work, providing 3-D warping functions and two-dimensional nonlinear constitutive relation for Nonlinear Finite Element Analysis of shells. Current theory and code are demonstrated through standard test cases and validated with literature. © Springer Nature Switzerland AG 2019.