A rotor and/or stator dampening system includes a stator and/or rotor with a liner selected of one or more materials to achieve a desired dampening effect. In one implementation, a progressive cavity motor or pump includes a stator with an internal axial bore therethrough. The stator has a liner along an axial length thereof with an inwardly facing surface defining the internal axial bore therethrough. The liner has a plurality of axial sections with at least two of the plurality of axial sections being constructed of different materials. A compression resistant mechanism, such as a spring or spring-like device, is disposed within at least one of the axial sections of the liner. The progressive cavity motor or pump also includes a rotor that is disposed and is rotatable within the internal axial bore of the stator to form a moving chamber between the rotor and the stator.