Costal cartilage is one of the load bearing tissues of the rib cage. Literature on the material characterization of the costal cartilage is limited. Atomic force microscopy (AFM) has been extremely successful in characterizing the elastic properties of soft bio-materials like articular cartilage and hydrogels, which is often the material of choice for cartilage models. But AFM data on costal cartilage is absent in the literature. In this thesis, AFM indentations using spherical beaded tips were performed on agarose gel and costal cartilage to isolate mechanical properties. A novel method was developed for modeling the relaxation indentation experiments based on Fung’s quasi-linear viscoelasticity (QLV) and a continuous relaxation spectrum. This particular model has been popular for uniaxial compression test data analysis. The QLV theory was extended for indentation relaxation data in this research effort. Using the model, elastic modulus of costal cartilage was found to be about 2 ~ 5 MPa and 0.93±0.09 kPa for 1% agarose gel. A large variation of modulus was observed over the tissue. Also, the modulus values decreased with distance from the costochondral junction. As a comparative study, macro-scale indentations were performed on costal cartilage. Using the QLV model, the macro scale modulus was found to be almost twice than the AFM modulus.