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This paper presents a novel probabilistic model of random uncertainties for dynamical system in the medium-frequency (MF) range. This approach combines a nonparametric probabilistic model of random uncertainties for the reduced matrix models in structural dynamics with a reduced matrix model adapted to the MF range. The theory is presented, the random energy matrix relating to a given MF band, its random trace and its random eigenvalues are studied. A numerical example is presented allowingdoi:10.1061/(asce)0733-9399(2003)129:9(1017) fatcat:vcrk2j2lofbpbontcr6kugmrc4