Abstract Pure neutron matter is not likely to be found in any of the Earth’s laboratories, but it has been found to exist as the material of neutron stars. It presents an interesting and difficult manybody problem which may be attacked by QMC methods. In this paper the authors report variational, approximate fixed-node, and released-node QMC calculations for uniform neutron matter in a three-dimensional box with periodic boundary conditions. These allow the determination of the energy E(p) as a function of the neutron density p for a realistic two-neutron interaction expression. The results are used to assess the accuracy of earlier variational approaches. The system treated was that of 14 neutrons in a cube at densities in the range of 1 / 4 to 3/2 the density p0 typical for nuclear matter. Most of the calculations were done for the Argonne v8’ two-body interaction potential. The trial wavefunction was a correlated Slater function, identical for the variational and diffusion calculations, specifying the nodes and used in importance sampling. Corrections were made for the effects of finite box dimensions. The released-node calculations were limited to very short time intervals especially for the higher densities. The energies E(p) found in the diffusion QMC calculations were 5 to 10% lower than those of the variational QMC. The releasednode results, with relatively large statistical errors, were not significantly different from the fixed-node results. The energies determined for the lower densities were estimated to be accurate within 2% and those for the higher densities somewhat less accurate. The results showed earlier predictions to be generally correct. Comparisons of results from variational chain summations (VCS) indicated an overall accuracy of about 10% for that method.