This paper deals with the torsional waves propagating in a pipe contacting with viscous liquid theoretically by supposing the flow is laminar. The dispersion and attenuation curves are investigated to determine the influence of viscosity of liquid on the torsional waves, and the relations between attenuation of first torsional mode and viscosity/density of liquid, for the application of torsional wave in non-destructive testing in pipes. The numerical results agree well with the experimental result in literature; the hypothesis of laminar flow is proved; and the advantages of first torsional mode wave in damage inspection are shown.