Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We present three new sets of C-1 hierarchical high-order tensor-product bases for conforming finite elements. The first basis is a high-order extension of the Bogner-Fox-Schmit basis. The edge and face functions are constructed using a combination of cubic Hermite and Jacobi polynomials with C-1 global continuity on the common edges of elements. The second basis uses the tensor product of fifth-order Hermite polynomials and high-order functions and achieves global C-1 continuity for meshes of quadrilaterals and C-2 continuity on the element vertices. The third basis for triangles is also constructed using the tensor product of one-dimensional functions defined in barycentric coordinates. It also has global C-1 continuity on edges and C-2 continuity on vertices. A patch test is applied to the three considered elements. Projection and plate problems with smooth fabricated solutions are solved, and the performance of the h- and p-refinements are evaluated by comparing the approximation errors in the L-2- and energy norms. A plate with singularity is then studied, and h-and p-refinements are analysed. Finally, a transient problem with implicit time integration is considered. The results show exponential convergence rates with increasing polynomial order for the triangular and quadrilateral meshes of non-distorted and distorted elements. Copyright (C) 2016 John Wiley & Sons, Ltd.1097936964Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)