The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave (fast compressional wave) by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed. The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave (fast compressional wave) by an infinite cylindrical shell deeply embedded in isotropic saturated soils is learned by may the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.