Two nonlinear interfacial elasticity models—interfacial elasticity decreasing linearly andexponentially with area fraction—are developed for the encapsulation of contrast microbubbles. Thestrain softeningdecreasing elasticityresults from the decreasing association between theconstitutive molecules of the encapsulation. The models are used to find the characteristic propertiessurface tension, interfacial elasticity, interfacial viscosity and nonlinear elasticity parametersfor acommercial contrast agent. Properties are found using the ultrasound attenuation measured througha suspension of contrast agent. Dynamics of the resulting models are simulated, compared withother existing models and discussed. Imposing non-negativity on the effective surface tensiontheencapsulation experiences no net compressive stressshows “compression-only” behavior. Theexponential and the quadraticlinearly varying elasticitymodels result in similar behaviors. Thevalidity of the models is investigated by comparing their predictions of the scattered nonlinearresponse for the contrast agent at higher excitations against experimental measurement. All modelspredict well the scattered fundamental response. The nonlinear strain softening included in theproposed elastic models of the encapsulation improves their ability to predict subharmonic response.They predict the threshold excitation for the initiation of subharmonic response and its subsequentsaturation.