  We construct thin shell wormholes in the magnetic Melvin universe. It is
shown that in order to make a TSW in the Melvin spacetime the radius of the
throat can not be larger than $\frac{2}{B_{0}}$ in which $B_{0}$ is the
magnetic field constant. We also analyze the stability of the constructed
wormhole in terms of a linear perturbation around the equilibrium point. In our
stability analysis we scan a full set of the Equation of States such as Linear
Gas, Chaplygin Gas, Generalized Chaplygin Gas, Modified Generalized Chaplygin
Gas and Logarithmic Gas. Finally we extend our study to the wormhole solution
in the unified Melvin and Bertotti-Robinson spacetime. In this extension we
show that for some specific cases, the local energy density is partially
positive but the total energy which supports the wormhole is positive.
