The present study addresses essentially to the investigation of the longitudinal vibrations of a stepped-pipe string for mining from deep-sea floors. The stepped-pipe string, consisting of four parts having different physical properties in each pipe string segment, is assumed to have two pump modules and a buffer, each of which is equipped with a vibration absorber. Moreover, the pipe string is subjected to external viscous damping because of the surrounding medium. A theoretical analysis has been made for a simplified model of the system, in which it is assumed that both the pump modules and buffer can be considered as concentrated masses, the fluid inside of the pipe string vibrates together with the string, and that the flexible pipe does not affect the vibration of the pipe string. Furthermore, absorbers are modeled as concentrated masses, each of which is attached to pump modules and the buffer by springs and dampers. Applying the method of separation of variables, exact analytical solutions for damped free and forced responses of the system subjected to heave motion of the mining ship are determined with and without absorbers, in which overdamped and underdamped modes are determined and studied separately too. It is important to note that the solutions obtained are expressed in terms of parameters characterizing the physical properties of the system under consideration. Numerical applications show that the attachment of convenient vibration absorbers causes the longitudinal displacements at the certain locations to decrease to very small values, where the vibration absorbers are adjusted to the excitation frequency. © 2004 Elsevier Ltd. All rights reserved.