The mechanical characteristics of graphene ribbons with an attached proof mass that can be used as NEMS transducers have been minimally studied, which hinders the development of graphene-based NEMS devices. Here, we simulated the mechanical characteristics of graphene ribbons with an attached proof mass using the finite element method. We studied the impact of force, residual stress, and geometrical size on displacement, strain, resonant frequency, and fracture strength of graphene ribbons with an attached proof mass. The results show that the increase of width and thickness of graphene ribbons would result in a decrease of the displacement and strain but also an increase of resonant frequency. The increase of the length of graphene ribbons has an insignificant impact on the strain, but it could increase the displacement and decrease the resonant frequency. The increase of residual stress in the graphene ribbons decreases its strain and displacement. The estimated fracture strength of graphene shows limited dependence on its thickness, with an estimated value of around 148 GPa. These findings contribute to the understanding of the mechanical characteristics of graphene ribbons with an attached proof mass and lay the solid foundation for the design and manufacture of high-performance graphene-based NEMS devices such as accelerometers.