As we are moving towards nano level devices, there is a greater need to miniaturize resonators. Miniaturization of resonators helps to attain higher sensitivity, lower power consumption, higher resonance frequency along with lesser requirement of space. Since graphene is strong and stiff and has various other exceptional mechanical properties, graphene based resonators are of interest. Most of the garphene resonators in the past have been measured using optical setup. In order to get rid of this large and bulky setup, we aim to integrate it with an actuation electrode. The main goal of this thesis is to fabricate an electrostatically actuated graphene resonator. For the graphene membrane to work as a resonator, it needs to be suspended. In this work, various samples of different shapes, sizes and gap sizes have been analyzed using different experiments. Some samples are found to be collapsed. Whereas the other samples show corrugations and wave like structure. We observe clear differences between the SEM and AFM images of the collapsed and likely suspended samples. This is followed by the fabrication of graphene resonator with a buried electrode. This work presents all the failed attempts to fabricate suspended graphene membrane on a buried electrode before realizing the suspended graphenes membrane on p doped polysilicon and niobium electrode. To find the resonant frequency of the graphene membrane, experiments such as DC tuning and nonlinearity have been performed on the samples. We found a high frequency peak becoming much more non linear at high oscillation amplitudes than the low frequency peak. We suspect it to be graphene's resonant frequency. In the later part of this work, the cause of the collapse of membranes is analyzed. Using stress measurements and observations from various samples, some hypothesis have been proposed for the collapsing graphene membranes. We also observed bubble like structures on graphene samples which formed suspended membranes after release. We have found the cause of collapse of membranes but the exact mechanism of suspension is still unknown. The EDX analysis on the bubbles show that the bubble area has significant amount of more oxygen than the other area of graphene. To use graphene membranes as a resonator, it needs to be fully suspended. Hence, it is crucial to understand the process of suspension of graphene in more detail.