Current clinical methods of reconstruction surgery involve laser reshaping of nasal cartilage. The process of stress relaxation caused by laser heating is the primary method to achieve nasal cartilage reshaping. Based on this, a rapid, non-destructive and accurate elasticity measurement would allow for a more robust reshaping procedure. In this work, we have utilized a phase-stabilized swept source optical coherence elastography (PhS-SSOCE) to quantify the Young's modulus of porcine nasal septal cartilage during the relaxation process induced by heating. The results show that PhS-SSOCE was able to monitor changes in elasticity of hyaline cartilage, and this method could potentially be applied in vivo during laser reshaping therapies.