Raman spectroscopy has been widely used for cancer diagnosis, but conventional forms provide limited depth information. Spatially offset Raman spectroscopy (SORS) can solve the depth issue, but it has only been used to detect hard tissues such as bone. We explore the feasibility of using SORS to discriminate two layers of soft tissue. Measurements were taken with individual source and detector fibers at a number of spatial offsets from samples consisting of various thicknesses of normal human breast tissues overlying breast tumors. Results show that SORS can detect tumors beneath normal tissue, marking, to the best of our knowledge, the first application of SORS for discriminating two layers of soft tissue.