A simple hexagonal array of classical spins coupled by nearest-neighbour antiferromagnetic Heisenberg interactions has a ground state with a triangular antiferromagnetic configuration of spins. We have developed spin wave theory for triangular antiferromagnets with both Heisenberg and dipole–dipole interactions. The dipole–dipole interactions confine the spins to the hexagonal basal plane and they do not distort the equiangular triangular structure. Spin wave dispersion relations are plotted for some trial values of the exchange constants. The theory is applied to the triangular antiferromagnet CsMnBr3. This is a quasi-one-dimensional material with strong exchange interactions along the hexagonal axes and with weak exchange interactions within the basal plane that are of the same order as dipolar interactions.