The elasticity of a Krull domain R is equivalent to the elasticity of the block monoid B(G,S), where G is the divisor class group of R and S is the set of elements of G containing a height-one prime ideal of R. Therefore the elasticity of R can by studied using the divisor class group. In this dissertation, we will study infinite divisor class groups to determine the elasticity of the associated Krull domain. The results will focus on the divisor class groups Z, Z(p infinity), Q, and general infinite groups. For the groups Z and Z(p infinity), it has been determined which distributions of the height-one prime ideals will make R a half-factorial domain (HFD). For the group Q, certain distributions of height-one prime ideals are proven to make R an HFD. Finally, the last chapter studies general infinite groups and groups involving direct sums with Z. If certain conditions are met, then the elasticity of these divisor class groups is the same as the elasticity of simpler divisor class groups.