An analytical solution for the stress analysis of superconducting sole
noids is given which reflects the full spatial variation of Lorentz bo
dy forces and includes shear stress components. The solution is based
on power series expansions of the Lorentz body forces and the displace
ments which in turn gives the strains and stresses, including shear st
ress components. This solution is applicable to the windings and reinf
orcement layers of magnets and is compared to a finite element method
using a 7 T sample magnet with reinforcement.