Observations of very long period elastic waves are attributed to 'silent' earthquakes, events which are presumed to occur at depth in a nonbrittle regime. The fault at depth is modeled as a thin viscoelastic gouge layer embedded in an elastic medium. The source of silent earthquakes is envisaged as a prolonged, slow slippage of the fualt faces, which yields a radiation spectrum strongly depleted in the high-frequency components and dominated by the near-field term. The results of the model are compared with the dominant frequencies, mean duration, and amplitude of a long-period perturbation recorded at Trieste in the years preceding the 1976 Friuli (Italy) earthquake. The role that silent earthquakes may play in the overall earthquake mechanism (in particular, as precursory phenomena) is discussed.