In Multilayered structures the interface effects have a wide range of applications in aerospace, automotive and especially in civil engineering. The design and construction of these structures and the account for interface effects require special expertise in modeling, simulation and implementation. Many studies in this case were conducted to address these issues. The objective of this work is the modeling and numerical simulation of static and dynamic behaviors of beams and plates multilayered structures with different types of interfaces. The focus was on the prediction of the behavior of stresses; shears and displacements depending on thickness. The interface can be elastic or viscoelastic of small or large thickness. The state space method has been developed for this purpose. Various types of rolled arbitrary number of isotropic or anisotropic layers structures were considered. The three-dimensional behavior is obtained for different types of static and dynamic loading. The results were compared with those based on the model of Stroh and on the various existing theories of beams and plates. The methodological approach, developed here, will be applied to thick structures, functionally graded, bimorph or multilayer structures and possibly piezoelectric or viscoelastic layered structures with interface effect