Elastic constants are important parameters to describe the mechanical properties of metal foils. To accurately measure the elastic constants of metal foils, a nondestructive testing method is proposed based on laser ultrasonic technology. First, the inverse problem of elastic modulus calculation is solved numerically. Second, the ultrasonic fields excited by a pulse laser on 20 μm thick foils of Mg-Li alloy, 304 stainless steel and 6061 aluminum alloy are calculated by the direct coupling finite element method. The simulated Lamb wave speed is brought into the numerical calculation program to get the calculation values of elastic modulus and Poisson''s ratio which are subsequently compared with the model specifications. Finally, the effectiveness of the numerical method for inverse problems is verified by the experimental measurement of aluminum alloy foils. The results show that the elastic modulus and Poisson''s ratio of foils can be accurately obtained by the numerical method. These results provide a certain reference for evaluating the mechanical properties of metal foils through the measurement of elastic constants.