The Percus-Yevick (PY), HNC, nonspherical bridge function (NSB), and VM integral equation theories are used to study the structure and thermodynamics of the hard linear homonuclear triatomic fluid. Results for the spherical harmonic coefficients of the pair distribution function and for the compressibility factor are compared with computer simulation data for a range of triatomic densities and elongations up to 1·6. The VM theory gives excellent results for the harmonic coefficients in the site-site and centre-site molecular coordinate frames, the PY theory results are fair, and the NSB and HNC theory results are poor at low distances. None of the theories satisfactorily describes theg000harmonic coefficient in the centre-centre frame in the vicinity of contact at high densities. The VM compressibility factors agree quantitatively with those of the simulations. The NSB equation of state results are also excellent. The PY values are too low and the HNC values are too high. The thermodynamic consistency of the VM theory is excellent, that of the NSB theory very good, and that of the PY and HNC theories poor, especially at high densities.