Transition radiation of elastic waves generated by a mechanical object that performs a uniform rectilinear motion along an inhomogeneous elastic system (a string, beam, membrane, or plate) is discussed in detail. The effect is analyzed by assuming that the law of motion of the load admits the generation of neither Cherenkov nor bremsstrahlung radiation and that the role of inhomogeneities is played by the supports of the elastic system. The radiation reaction spectrum and the loss of contact between the object and the elastic system are considered.The practically important cases of periodically and randomly varying elastic parameters are examined, and the resonance and instability conditions for the vibrations of the radiating object are found. Variation of the main radiation characteristics with the angle at which the object crosses the inhomogeneity region is examined. The so-called diffraction radiation of elastic waves is briefly discussed.