We propose a method for measuring surface shapes of transparent objects by using a polarizing filter. Generally, the light reflected from an object is partially polarized. The degree of polarization depends upon the incident angle, which, in turn, depends upon the surface normal. Therefore, we can obtain surface normals of objects by observing the degree of polarization at each surface point. Unfortunately, the correspondence between the degree of polarization and the surface normal is not one to one. Hence, to obtain the correct surface normal, we have to solve the ambiguity problem. In this paper, we introduce a method to solve the ambiguity by comparing the polarization data in two objects, i.e., normal position and tilted with small angle position. We also discuss the geometrical features of the object surface and propose a method for matching two sets of polarization data at identical points on the object surface.