Flexibility of graphene (Gr) is partially credited to its two-dimensional (2D) molecular structure which resembles like interconnected unit of hexagonal carbon atoms ring. Therefore, to increase the flexibility of micromechanical beams, we analyze the influence of hexagonal shape of microcantilever beam without and with hexagonal hole of varying side length. To carry out the analysis, we first fabricate the hexagonal structure and perform measurement using laser vibrometer. Based on the measurement, we found that the presence of hexagonal holes make the beam flexible by two order of magnitude more than that of a conventional beam without holes. However, we found that the frequency of microcantilever beam with hexagonal shape decreases with increase in hole size. To undo the effect of hexagonal holes on microbeam frequency, we cover the microbeam with an electrospun cellulose acetate nanofiber mat (CAF). Based on the measurements, we found that the frequency can be increased more than that of a solid rectangular microbeam. Finally, we propose a finite element based methodology to model microbeam and nanofiber mat to compute their frequencies. Thus, based on the understanding developed in this work, this hierarchical structure of microcantilever beam with electrosun nanofibers can be used as a best candidate for utilizing it for the development of flexible sensors based on MEMS devices. © 2019 IOP Publishing Ltd.