The analysis of flat plates under general constraints remains an open problem in the scientific community, which can only be addressed computationally. In this study we introduce a novel computational method for the linear static analysis of two-dimensional macro-elements with special reference to triangular shape, usable for modeling complex structures by assembling them as macro-elements. In particular, we analyze the bending behavior of the single generic macro-element according to the Kirchhoff model. The boundary conditions are expressed exclusively in terms of static equilibrium and the constraints consist of elastic springs distributed along the boundary and having finite stiffness. Our method allows for the continuous modeling of the elements without discretizing the domain (as in the finite element method FEM). To achieve this, the procedure assumes a displacement field that exactly satisfies the field equations. Specifically, the displacement field is defined as sum of a particular solution and a linear combination of kernel biharmonic functions with unknown coefficients. The principle of virtual work enables to determine the governing equations, which, for the assumed displacement field, reduce to the weak form of the boundary conditions. Objective of our study is to evaluate the performance of the proposed procedure by varying the number of coefficients used, the choice of the kernel basis and the stiffness value of the almost rigid constraints (which replace the purely kinematic and therefore infinitely rigid constraints), in terms of efficiency and accuracy. Finally, preliminary results confirm that the achieved solution exactly solves the field equation providing, at the same time, a good approximation for the boundary conditions.