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Non-conforming membrane elements which have variable number of mid-side nodes withdriling degrees of fredom and which is designated as NMDx have been presented in this paper. Thenon-conforming elements with variable number of mid-side nodes can be efficiently used in the localmesh refinement for the in-plane structures. To guarante the developed elements always pas the patchtest, the direct modification method is incorporated into the element formulation. Detailed numerical testsin this study show the validity of the variable node NC elements developed in this study and a wideapplicability of these elements to practical problems.