The magnet support system of the Wendelstein 7-X (W7-X) fusion stellarator includes challenging components, called Narrow Support Elements (NSEs), placed between the Non Planar Coils (NPCs) at the inboard side and aimed at reducing deformation of the coils. NSEs are small contact elements, with special coating to reduce friction, that have to withstand high compressive and shear forces. The objective of this article is to demonstrate the structural reliability of the NSEs under electromagnetic loading (EML), taking into account in a conservative way the relevant material properties at cryogenic temperatures. To this purpose, an appropriate parametric local Finite Element (FE) model of one highly loaded NSE with its components (pad, pad frame and counter pad) and of a portion of the coils has been developed with ABAQUS code and isotropic elastic-plastic material model with hardening/softening has been used, in order to include the serration effect at 4K. Different mechanical limit analyses have been performed including consecutive steps of shrink fitting the NSEs in the coils, cooling down to 4K and gradual increasing of the coil displacements induced by the EML.