One dimensional fluid equations are examined together with Poisson's equation for an ion beam-plasma system by taking the boundary conditions into account, as was done by Pierce1) for an electron beam. A dispersion relation obtained shows that an ion acoustic wave and the beam waves split into many unstable new modes even if they are stable in an unbounded system. Their frequencies as well as the growth rates depend largely on the length L of the system. The frequencies decrease monotonously with increasing the value of ωpiL/Vo. Meanwhile, the growth rates appear at certain values of ωpi L/Vo, and they attain to their maximum values at respective different ones and then decrease gradually. The dependences of their frequencies and the growth rates on the drift velocity Vo and the number density Nb of the beam are also examined.