The mechanical properties of thin-film Li-ion battery electrodes are controlled by the micro structure of the constituent materials. In this work, a non-contact and non-destructive measurement of the mechanical properties of electrode films is performed by measurement of zero group velocity (ZGV) resonances. The ZGV Lamb wave modes of a solid bi-layer consisting of a thin metallic layer and a thin compliant coating layer are shown to be dependent on the Young's moduli, thicknesses, densities and Poisson ratios of the layers. Theoretical models are used to quantify the sensitivity of the ZGV resonances to changes in mechanical properties. Experimental ZGV resonances are excited using a pulsed infrared laser and detected using a laser interferometer. Commercial-grade battery films with different coating materials, densities and thicknesses are measured. Young's moduli of the battery electrode layers are estimated using the combination of a theoretical model and experimental results. The effect of the calendering process on the battery materials is also investigated. Results suggest that the Young's modulus of the electrode coating increases drastically after the battery films are calendered. This technique can be used to quantitatively study the mechanical properties of Li-ion battery electrodes to improve overall battery performance.