Atomistic models of polybutadiene have been generated using molecular mechanics and molecular dynamics at a bulk density of 0.89 g cm-3. Four microstructures formed by cis-1,4-polybutadiene, trans-1,4-polybutadiene, 1,2-polybutadiene, and a random copolymer of the three (55% trans, 35% cis, and 10% vinyl) are analyzed for static free volume. The free volume is determined by hard spherical probes that see the atoms as hard spheres of radii which equal 89% of their van der Waals radii. The total free volume, the free volume distribution, and the shape of the voids are analyzed for all four microstructures. The accessible free volume as a function of the probe size is found to be characteristic of voids in disordered packings of hard spheres. The free volume distributions have some common features across the microstructures. In particular, the free volume distributions as probed by a 1-angstrom radius probe show void size concentrations around approximately 7.5 and 15 angstrom3 (with the exception of trans-polybutadiene, which does not display the latter). The shape factors for all four structures decay to the same asymptotic value of 0.67 +/- 0.1 over the size range of 0-5 angstrom3. There is a marked difference in the asphericity and the acylindricity of voids in the four microstructures. Analysis of randomly generated shapes suggests that the voids in the polymer microstructures are mostly elongated in comparison with randomly "grown" cavities, probably due to the connectivity of the polymer chains.