The longitudinal electromagnetic interaction of an intense coasting beam with itself, including the effect of a resistive vacuum tank, is investigated theoretically. It is shown that even in the range where the particle frequency is an increasing function of particle energy, the beam can be longitudinally unstable due to the resistivity of the vacuum tank walls. In the absence of frequency spread in the unperturbed beam the beam is shown to be always unstable against longitudinal bunching with a growth rate which depends upon (N/{sigma}){sup 1/2}, where N is the number of particles in the beam and {sigma} is the conductivity of the surface material. By means of the Vlasov equation, a criterion for stability of the beam is obtained; and shown in the limit of high-conductivity walls to involve the frequency spread in the unperturbed beam, the number of particles N, the beam energy, geometrical properties of the accelerator, but not the conductivity {sigma}. A numerical example is presented which indicates that certain observations of beam behavior in the MURA 40 MeV electron accelerator may be related to the phenomena investigated here.