The boundary value problem for a superconductor has been solved for specific axially symmetric geometries. The interior field of a right circular shell is found to be quite uniform. Also it is found that the ends of the shell can be shaped to overcome a singularity at the end. This permits a near critical and uniform field to be obtained over a very large volume of the central region. Experimentally it was found that a simple geometric shape electrolytically coated with lead would trap a field of 630 gauss with homogeneity in agreement with calculation.