Application of the Two-Dimensional Hermitian Finite- Difference Method to Linear Shear  Deformation Theory of Plates and Arbitrarily Curved Shells H.Wimmer, Innsbruck, Austria Starting from the linear, partial differential equations of thin shell theory  including the effect of transvere shear deformations a matrix formulation  is presented in which all kinematic and dynamic variables appear as  differential quotients of first order. The transformation of the local field equations into an algebraic form  by  appropriate two-dimensional finite-difference operators leads to an  unsymmetrical banded algebraic equation system from which all  variables requested are directly evaluated. The constitutive equations take into consideration a symmetrically  layered cross section consisting of tangentially isotropic and  transversally orthotropic material. Because of the kinematic  assumptions of first approximation shell theory the deformation of the  cross section can be seized in an integral sense only. Since the basic equations are formulated in tensor notation with the  procedure presented shells of arbitrary curvature may be analyzed, of  which surface is given as an analytic continuosly differentiable function.  The algorithm pointed out shows good convergence attributes. Its  efficiency is demonstrated by two examples of which analytical solutions  are known.