In the present study, a finite element computational model for the nonlinear analysis of shell structures is presented. A tensor-based finite element formulation is presented to describe the mathematical model of a shell in a natural and simple way by using curvilinear coordinates. In addition, a family of high-order elements with Lagrangian interpolations is used to avoid membrane and shear locking, and no mixed interpolations are employed. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness stretching and, therefore, 3D constitutive equations are utilized. Numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composites, as well as functionally graded shells, are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation of shells. © 2006 Elsevier B.V. All rights reserved.