This paper suggests a new analysis algorithm for the time historical response of three dimensional rectilinear structure which is frequently found in a pipe line system of plant by the combination of the transfer stiffness coefficient method(TSCM) and the Newmark method. The present analysis algorithm for a time historical response can improve the computational accuracy and time remarkably owing to advantages of the TSCM in comparison with transfer matrix method(TMM). The structural system is modeled as a lumped mass system in this method. The analysis algorithm was formulated far the three dimensional rectilinear structure. We confirmed the validity of the present algorithm by comparing the numerical computation results of TSCM with those of TMM.