A micro-electro-mechanical (MEM) beam and column structures are analysed in details in the present work containing fixed charge (+ve or −ve). The transverse deflection of this column, due to the presence of fixed-charge concentration and axial compressive force, is firstly studied (linear elastic and viscoelastic cases). An analytical solution of critical buckling load P supported by MEM column, with initial imperfections due to the presence of fixed-charge in the column (simply-supported), is derived. The variation of P with fixed-charge concentration is finally obtained. A pull-in instability of MEM beam is secondly studied under the influence of external electric field, and a critical voltage V without any instability is obtained varying fixed-charge concentration inside beam. All the presented formulations are extended incorporating finite deformation (von Kármán strain field) setting, as the beam rotation becomes significant at higher fixed-charge values. All the presented results are also verified with the published literature wherever it was possible. The presented work thus can be reasonably employed in the design of MEM micro-switches. © 2020 Elsevier Ltd