An analysis of magnetic shielding effectiveness of multilayered structures versus frequency is presented. It is shown that the quasistatic field approximation is accurate until several MHz depending on the source-to-observation-point distance, characteristic dimensions of the source, and physical and geometrical properties of layers. The accuracy is assessed by means of comparisons with the solution of the wave equation in a wide frequency reange. This study can be useful for the shield design and also for predicting the shielding effectiveness of multilayered magnetic shields in a source of non sinusoidal periodic magnetic fields.