Using the method of molecular dynamics it is shown that glasses can be formed from a 216 particle sample of the Lennard-Jones (LJ) liquid either by isobaric cooling or by isothermal compression. The properties of the glasses are relatively independent of the mechanism of formation. At zero pressure a glass transition, characterised by the disappearance of diffusion, occurs at ρ*=Nσ³/V= 0.98 and kT/ε= 0.29 (ρ* is a reduced density and V is the volume of the N-particle system; σ and ε are LJ parameters). The non-Arrhenius temperature dependence of diffusion coefficients in the metastable liquid and the changes of second order thermodynamic properties characteristic of the transition are discussed in relation to laboratory glass-forming systems. For isothermal compression near the normal melting temperature a glass transition occurs at ρ*= 1.06 and ρσ³/Nε= 8.8, where p is the pressure, although in this case it is less well-defined since crystal nucleation more readily occurs at higher temperature. Comparisons using perturbation theory show that the LJ system is ≈ 12% more dense at the glass transition than the equivalent hard sphere fluid. Analysis of radial distribution functions suggests that upon cooling and/or compression the soft LJ system can achieve a more compact second nearest neighbour packing geometry than hard spheres and may provide a better basis for modelling glass formation in, for instance, metal–metalloid systems.