Various models of systems of partial differential equations on multiples structures made of a finite number of interconnected flexible elements like strings, beams, shells, plates or combination of them have been recently proposed. Up to now, existence results of such problems have been given for each model and have clearly some similarities. Therefore the main goal of this work is to present a general framework as large as possible to include the former two-dimensional models. More precisely, we study transmission problems for elliptic systems of P.D.E.'s on twodimensional polygonal networks with general boundary and interface conditions.