Biological soft and fluid tissues, due to the high percentage of water, are nearly incompressible and consequently their velocity fields are nearly divergence-free. The two most commonly used types of vector field representation are piece-wisecontinuous representations, which are used in the finite element method (FEM), and discrete representations, which are used in the finite difference method (FDM). In both FEM and FDM frameworks divergence-free vector fields are approximated, i.e. they are not exactly divergence-free and both representation types require a relatively large number of degrees freedom. We showed that a continuous, divergence-free vector field model can effectively represent myocardial and blood velocity with a relatively small number of degrees of freedom. The divergence-free model consistently outperformed the thin plate spline model in simulations and applications with real data. The same model can be used with other incompressible solids and fluids.