Construction of homogeneous single-grid and composite double-grid curvilinear finite elements for calculating parameters of three-dimensional cylindrical panels and shells is presented. In this paper, stiffness matrix and nodal forces of curvilinear finite elements are determined in local Cartesian reference systems. The set of equations of finite element method for discrete models of shells and panels utilizes global Cartesian reference system. Relation between local and global coordinate systems is carried out using the rotation matrix defined only for vectors of curvilinear finite elements nodal displacements. Relations for finite element characteristics of cuboid for further displacement approximation are based on known polynomials and equations of threedimensional elasticity problem in local Cartesian reference system. The proposed single-grid and double-grid curvilinear elements provide three-dimensional stress state description while taking into account complexity of attaching and loading. Double grid curvilinear elements consider the heterogeneous and micro-inhomogeneous structure of panels and shells and serve as the basis for discrete models of small dimension.