The paper deals with aspects of the complexity of mechanical properties of porous structures made from copper fibers and fibers reinforced with copper meshes to assess the adhesive strength of the fibrous structure and the cohesion between the components of the tested elements used for the construction of heat exchangers. All of the tested samples were characterized by macroscopic open porosity. The internal structure of the obtained connections was analyzed by metallographic techniques. Statistical relations of the connections made between the layers have been provided. The side effects of the production technology related to the “hydrogen disease” of copper have been discussed.