A first-order shear deformation shell theory (FSDT), based on general curvilinear coordinates, has been reconstructed through a strain energy transformation. Based on the definition of the mean displacements, the transverse shear strains that are constant through the thickness are improved to vary through the thickness. It is assumed that the displacements and in-surface strains of three-dimensional theory are approximated by those of FSDT. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT relations. The present approach has been applied to a higher-order zigzag shell theory. Comparisons of displacements and stresses of laminated and sandwich shells using the present theory are made with the original FSDT and three-dimensional exact solutions.