We introduce precomputed multizone elastokinematic models for interactive simulation of multibody kinematic systems which include elastostatic deformations. This enables an efficient form of domain decomposition, suitable for interactive simulation of stiff flexible structures for real time applications such as interactive assembly. One advantage of multizone models is that each zone can have small strains, and hence be modeled with linear elasticity, while the entire multizone/multibody system admits large nonlinear relative strains. This permits fast capacitance matrix algorithms and precomputed Green's functions to be used for efficient real time simulation. Examples are given for a human finger modeled as a kinematic chain with a compliant elastic covering.