Publisher Summary This chapter discusses the nonlinearly elastic flexural shells. It identifies and mathematically justifies the two-dimensional equations of a nonlinearly elastic flexural shell. A nonlinearly elastic shell with middle surface S is considered, subjected to a boundary condition of place along a portion of its lateral face with θ(γ0) as its middle curve, where γ0 ⊂ γ. Such a shell is a nonlinearly elastic flexural shell if the manifold contains nonzero elements and possesses nonzero tangent vectors at each one of its points. The stored energy function of a nonlinearly elastic flexural shell is a quadratic and positive definite expression in terms of the exact difference between the curvature tensor of the deformed middle surface and that of the undeformed one, on one hand. The chapter establishes the existence of a solution to the minimization problem. The proof, which is based on the fundamental theorem of the calculus of variations, essentially hinges on a careful analysis of the properties of admissible inextensional displacements in H2(ω).