Plasma wake-field excitation by a train of relativistic electron bunch
es is studied analytically and computer simulated. Both the self-consi
stent particle bunch dynamics for Linear plasma response and the excit
ation of nonlinear plasma waves by the train of given bunches are cons
idered. The maximum field values and the size of the region where thes
e fields are excited are obtained as functions of the number of bunche
s.