Recent studies in mechanobiology have revealed the importance of cellular and extracellular mechanical properties in regulating cellular function in normal and disease states. Although it is established that cells should be investigated in a three-dimensional (3-D) environment , most techniques available to study mechanical properties on the microscopic scale are unable to do so. In this study, for the first time, we present volumetric images of cellular and extracellular elasticity in 3-D biomaterials using quantitative micro-elastography (QME). We achieve this by developing a novel strain estimation algorithm based on 3-D linear regression to improve QME system resolution. We show that QME can reveal elevated elasticity surrounding human adipose-derived stem cells (ASCs) embedded in soft hydrogels. We observe, for the first time in 3-D, further elevation of extracellular elasticity around ASCs with overexpressed TAZ; a mechanosensitive transcription factor which regulates cell volume. Our results demonstrate that QME has the potential to study the effects of extracellular mechanical properties on cellular functions in a 3-D micro-environment.