The microsensor is modeled as a two-layer micro beam in which the first layer is quartz and the second layer is silicon. This beam is clamped-free and beam has a rectangular cross-section. Sensitivity and quality factors which are two important functions in sensors are selected as objective functions. Dimensions of the micro beam are design variables, so this optimization has two functions and four variables of the design. Objective functions are depended on the natural frequency, material properties, and dimensions of the beam. The natural frequency is obtained according to the modified couple stress theory by using Rayleigh’s method. Optimization is done by using genetic algorithm. Results show the length of the beam has a significant effect on the sensitivity and quality factor. Also, it can be seen that when dimensions of the beam decrease, sensitivity increases, and quality factor decreases. Results are presented based on non-classical and the classical theories.