Brake squeal is uncomfortable noise that occurs while braking. It is an important issue for automobile quality to prevent brake products from squealing. Brake shims are widely used to reduce squeal occurrence rate. In particular, laminated shims can effectively suppress squeal via the viscoelastic damping of an adhesive layer. However, there are cases where the damping performance at low temperature and the durability performance at high temperature deteriorate. In that regard, we thought of applying frictional damping to shims instead of relying on a temperature-sensitive adhesive layer. To study the application of frictional damping as a new damping mechanism for shims, it is necessary to clarify the characteristics thereof. In order to quantify the damping performance of shims, loss factor has been generally measured with a bending mode tester. However, the influence of friction cannot be evaluated because it is measured under pressure-free condition. Therefore, we developed a new device that can measure damping of shims under pressing condition and evaluated the basic characteristics of frictional damping. To quantify the frictional damping, the developed method calculates the total energy loss from the area of hysteresis in a cycle of force-displacement oscillation. In addition, the influence of friction on damping is analyzed from the shape of the hysteresis loop. In this paper, we report the results of comparing laminated shims against textile fabrics, which served as samples for evaluating frictional damping. As a result of measurement by the developed method, it was confirmed that the amplitude and load dependency of the laminated shim was small, while on the other hand, the textile fabric has characteristics that damping increases with large amplitude and low load.