This work is related  to the inverse problem in vibration produced in a special type of mechanical structure known as periodic structure. This problem consist in determining the stiffness and mass parameter of the structure from the natural frequencies and vibrations modes. The problem concern with the inverse eigenvalue problem for a specially structured Jacobi matrix which contains the desired parameters. Necessary conditions to be applied to the data to obtain a real system are derived and a numerical procedure is develop. Some numerical examples are presented