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 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

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... lized 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.