By a transfer matrix-Newmark formulation iteration method, shock response analysis in time domain was performed for a propulsion shaft subjected to base-transferred shock excitations. In order to eliminate the numerical instability of TMT, the transfer vector is used, instead of the traditional one. Influences of gyroscopic effect and initial stress on response were investigated. Main conclusions are that gyroscopic effect has no obvious effect on shock response. Initial stress increases the total shock response, but the total response isn’t equal to the absolute sum of initial stress and shock excitations acting alone. Both ends of the shaft, that are propeller and thrust bearing locations, are weaker to bear shock excitations. Maximum amplitude of response occurs at the propeller location.