Based on the self-reference feature of the shearing interference, a lateral shearing interferometer is proposed for on-machine precision surface measurement. This shearing interferometer is based on a specially designed shear generator made of a single birefringence plate. Due to the self-reference feature and a common path polarized interference design which is based on the birefringence shear generator, the interferometer is simple and compact in structure. As a wave interferometer, the design has immunity to mechanical vibrations while it has high accuracy for precision surface measurement. The interferometer is suitable for on-machine precision surface monitoring for quality control. The principle of the proposed interferometer is introduced. Analysis and experimental testing were carried out. The results show that the interferometer has a good anti-vibration performance. The accuracy in RMS is better than λ/80.