Application of compressional optical coherence elastography (OCE) for delineation of tumor and peri-tumoral tissue with simultaneous assessment of morphological/molecular subtypes of breast cancer is reported. The approach is based on the ability of OCE to quantitatively visualize stiffness of studied samples and then to perform a kind of OCE-based biopsy by analyzing elastographic B-scans that have sizes ~several millimeters similarly to bioptates used for "gold-standard" histological examinations. The method relies on identification of several main tissue constituents differing in their stiffness in the OCE scans. Initially the specific stiffness ranges for the analyzed tissue components (adipose tissue, fibrous and hyalinized tumor stroma, lymphocytic infiltrate and agglomerates of tumor cells) are determined via comparison of OCE and morphological/molecular data. Then assessment of non-tumor/tumor regions and tumor subtypes is made based on percentage of pixels with different characteristic stiffness ("stiffness spectrum") in the OCE image, also taking into account spatial localization of different-stiffness regions. Examples of high contrast among benign (or non-invasive) and several subtypes of invasive breast tumors in terms of their stiffness spectra are given.