The propagation of torsional shock waves in a thin circular viscoelastic rod is investigated theoretically. An analysis is carried out based on the approximate equations previously derived. Two typical viscoelastic models are considered, which possess, respectively, the discrete and continuous relaxation spectrum. One is the usual Maxwell- Voigt model and the other is a new model whose relaxation function is given by a power law with weak singularity. The structures of steady shock profiles are presented and compared for both types. Finally a brief discussion is included on the simplified evolution equations for a far field transient behavior.

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