A solution is obtained to the problem of the longitudinal vibration of a rod with a coating. The solution is obtained in a refined formulation. The same theoretical model is also used to find the solution for the case of static tension. An analysis is made of the way in which the properties of a deformable rod are affected by the stiffness of the shear constraints, which is regarded as a physicomechanical characteristic of the coating-substrate system. A method is proposed for experimental determination of stiffness for both static and cyclic loading conditions. All of the relations needed to analyze the stress-strain state are presented, including those required for fatigue tests in tension-compression.