The asymmetry in the shapes of folded and unfolded states are probed using two parameters, one being a measure of the sphericity and the other that describes the shape. For the folded states, whose interiors are densely packed, the radii of gyration (Rg) and these two parameters are calculated using the coordinates of the experimentally determined structures. Although Rg scales as expected for maximally compact structures, the distributions of the shape parameters show that there is considerable asymmetry in the shapes of folded structures. The degree of asymmetry is greater for proteins that form oligomers. Analysis of the two- and three-body contacts in the native structures shows that the presence of near equal number of contacts between backbone and side-chains and between side-chains gives rise to dense packing. We suggest that proteins with relatively large values of shape parameters can tolerate volume mutations without greatly affecting the network of contacts or their stability. To probe shape characteristics of denatured states we have developed a model of a WW-like domain. The shape parameters, which are calculated using Langevin simulations, change dramatically in the course of coil to globule transition. Comparison of the values of shape parameters between the globular state and the folded state of WW domain shows that both energetic (especially dispersion in the hydrophobic interactions) and steric effects are important in determining packing in proteins.