The repulsive longitudinal space‐charge forces between particles being accelerated in a linac weaken the total phase‐focusing force which arises from the rf accelerating field. The stable longitudinal phase‐space area decreases as the particle phase‐space density increases. In this paper the techniques used in Nielsen and Sessler's treatment of the longitudinal space‐charge problem in circular accelerators are applied to the longitudinal space‐charge problem in linacs. A method for determining the dependence of the available longitudinal phase‐space area on the beam current is outlined. An example is worked out using the parameters of a linac designed at MURA for various values of stable phase angle, drift‐tube hole radius, and beam radius. Numerical results show that there is a significant decrease in stable longitudinal phase‐space area for instantaneous beam currents larger than about 100–200 mA.