A method for measuring the moduli of elasticity of material is presented in this paper. Laser frequency is locked-in the passage peak of Fabry-Perot etalon. Using the optical resonat characteristic of Fabry-Perot etalon with the optical beat frequency method, we can get the moduli of elasticity by measuring the strain under very small stress action. The relative errors of stress and stretch elastic moduli of quartz are given.