It has been accepted that the dynamic responses of ultrasound contrast agent (UCA) microbubbles will be significantly affected by the encapsulating shell properties (e.g., shell elasticity and viscosity). In this work, a new model is proposed to describe the complicated rheological behaviors in an encapsulating shell of UCA microbubbles by applying the nonlinear 'Cross law' to the shell viscous term in the Marmottant model. The proposed new model was verified by fitting the dynamic responses of UCAs measured with either a high-speed optical imaging system or a light scattering system. The comparison results between the measured radius-time curves and the numerical simulations demonstrate that the 'compression-only' behavior of UCAs can be successfully simulated with the new model. Then, the shell elastic and viscous coefficients of SonoVue microbubbles were evaluated based on the new model simulations, and compared to the results obtained from some existing UCA models. The results confirm the capability of the current model for reducing the dependence of bubble shell parameters on the initial bubble radius, which indicates that the current model might be more comprehensive to describe the complex rheological nature (e.g., 'shear-thinning' and 'strain-softening') in encapsulating shells of UCA microbubbles by taking into account the nonlinear changes of both shell elasticity and shell viscosity.