The paper presents a new way to determine some dynamical properties of materials modeled by the so-called degenerate system. The system is an element (subsystem) of any complex multidegree-of-freedom system. This subsystem follows from assumption of standard rheological model of stress–strain law of the materials. It is assumed that on the complex system act a set of random excitation forces. For this coincidence, a so-called energy balance equation was developed and was used to create a suitable identification method. The equations were derived for any differentiable function of elasticity. The stationary random process of the system response was assumed in the whole algorithm. As it was proved, in this case, instead of calculating appropriate fields of the hysteresis loop of suitable signals, an application of average values of the input and output signals and their proper combinations can be used. It is assumed that the elastic damping interaction force in the complex dynamical subsystem is described by the function $F(x,x\u02d9)$, in which x is a deformation of the identified degenerated element and denotes a relative displacement between some appropriate neighboring masses of the system. Some numerical examples of the application are shown.