The work aims to propose a surface acoustic wave (SAW) method for surface strain detection of packaging materials and design a demodulation method of SAW strain sensor with high precision based on SVD-Rife algorithm. SVD method was used to denoise the SAW resonator echo signal in order to improve the demodulation accuracy. Based on Rife algorithm, a spectral subdivision estimation method was designed, which could lower the hardware requirements of the system and improve the spectral estimation accuracy. The demodulation method designed was simulated and experimented. The simulation results showed that, the estimated variance was improved and the maximum error was 0.25 kHz. Finally, the proposed SAW strain sensor was tested. The linearity of the sensor was 1.45% and the repeatability was 1.09%. Compared with the traditional demodulation method, the linearity of the sensor was improved. The experimental results show that the demodulation method designed can be used to detect the surface strain of packaging materials.