In this paper, the finite element method is used for an eigenvalue analysis of a prestressed force sensor. The proposed force sensor is a 2x2 mm2 silicon nitride membrane 50 nm thick, with and without an additional platinum layer. The study uses FEMAP software with NX Nastran solver to derive the finite element model of the square membrane clamped on all four edges. Eigenfrequencies of a prestressed force sensor, with and without an additional platinum layer are determined. Also, the eigenfrequencies of a stress-free force sensor, with and without an additional platinum layer are determined. Results showed that the eigenfrequencies of a prestressed force sensor with 10 nm platinum layer are 23% lower than the eigenfrequencies of a prestressed force sensor without platinum layer. Further, eigenfrequencies of a stress-free force sensor with 10 nm platinum layer are 20% lower than the eigenfrequencies of a stress-free force sensor without platinum layer, which led to the conclusion that platinum coating increases sensor's sensitivity. Also, the impact of the non-symmetrical distribution of platinum on the eigenfrequencies of a prestressed force sensor was investigated, which showed that the non-symmetrical application of platinum on the sensor reduces the number of degenerate vibration modes of the membrane. And finally, the influence of different levels of prestress on the eigenfrequencies of the force sensor was examined from which it was concluded that with an increase in the thickness of the platinum, the prestress that the membrane can withstand decreases because the platinum atoms damage the sensor's surface.