A new elastic element of fiber Bragg grating accelerometer which is four peripheral clamped trapezoidal beams is developed. On the basis of analyzing the mechanical condition of this elastic element, the theoretical model is obtained. Furthermore, the degree of strain uniformity of the beam will be discussed. The elastic element has nearly uniform stain near the fixed end , where can be as grating area. This kind of elastic element not only can be used with fiber Bragg grating accelero- meter, but also other types of sensors.