Summary: Numerical simulations of the one-dimensional Newtonian four-body problem have been conducted for the special case in which the bodies are distributed symmetrically about the centre of mass. Simulations show a great similarity between this problem and one-dimensional Newtonian three-body problem. As in that problem, the orbits can be divided into three different categories which form well-defined regions on a Poincaré section: there is a region of quasiperiodic orbits about a Schubart-like periodic orbit, there is a region of fast-scattering encounters, and in between these two regions there is a chaotic scattering region. The Schubart-like periodic orbit’s stability to perturbation is studied. It is apparently stable in one dimension, but is unstable in three dimensions.