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Encapsulated microbubbles (EMBs) are widely used to enhance contrast in ultrasound sonography and are finding increasing use in biomedical therapies such as drug/gene delivery and tissue ablation. EMBs consist of a gas core surrounded by a stabilizing shell made of various materials, including polymers, lipids and proteins. We propose a novel model for a spherical EMB that utilizes a statistically-based continuum theory based on transient networks to simulate the encapsulating material. The use of transient network theory provides a general framework that allows a variety of viscoelastic shell materials to be modeled, including purely elastic solids or viscous fluids. This approach permits macroscopic continuum quantities – such as stress, elastic energy and entropy – to be calculated locally based on the network configuration at a given location. The model requires a minimum number of parameters that include the concentration of network elements, and the rates of attachment and detachment of the elements to and from the network. Using measured properties for a phospholipid bilayer, the model closely reproduces the experimentally-measured radial response of an ultrasonically-driven, lipid-coated microbubble. The model can be readily extended to large nonspherical EMB deformations, which are important in many biomedical applications.