This paper presents Best Theory Diagrams (BTDs) constructed from non-polynomial terms to identify best shell theories for bending analysis of cross-ply single skin and sandwich shell panels. This structure presents a constant radii of curvature. The shell theories are constructed using Axiomatic/Asymptotic Method (AAM). The different shell theories are described using the Carrera's Unified Formulation. The governing equations are derived from the Principle of Virtual Displacement (PVD). Navier-Type closed form solution is used for solving the bending problem of simply supported doubly curved shell panels subjected to bi-sinusoidal transverse pressure. The BTDs built from non-polynomial functions are compared with Maclaurin expansions. Spherical shell panels with different layer-configurations are investigated. The results demonstrated that the shell models obtained from the BTD using non-polynomial terms can improve the accuracy obtained from Maclaurin expansion for a given number of unknown variables of a displacement field.