Molecular dynamics simulation of a linear soft polymer has been performed and the free volume properties of the system have been analyzed in detail in terms of the Voronoi polyhedra of the monomers. It is found that there are only small density fluctuations present in the system. The local environment of the monomers is found to be rather spherical, even in comparison with liquids of atoms or small molecules. The monomers are found to be, on average, eight coordinated by their nearest geometric neighbors, including intra-chain and inter-chain ones. The packing of the monomers is found to be rather compact, in a configuration of 1900 monomers there are, on average, only three voids large enough to incorporate a spherical particle as large as a monomer, indicating that the density of the large vacancies in the system is considerably, i.e., by a few orders of magnitude lower than in molecular liquids corresponding to roughly the same reduced densities. (C) 2004 American Institute of Physics.