We propose a method for estimating the stiffness of bio-specimens by measuring their linear retardance properties under applied stress. For this purpose, we employ an epi-illumination Mueller matrix microscope and show the procedures for its calibration. We provide experimental results demonstrating how to apply Mueller matrix data to elastography, using chicken liver and chicken heart as biological samples. Finally, we show how the histograms of linear retardance images can be used to distinguish between specimens and quantify the discrimination accuracy.