The solar convection zone is a turbulent plasma interacting with a magnetic field. Its magnetic field is often
described as fibrillar since it consists of slender flux tubes occupying a small fraction of the total volume. It is
well known that plasma flow will exert a force on these magnetic fibrils, but few models have accounted for
the back-reaction of the fibrils on the flow. We present a model in which the back-reaction of the fibrils on the
flow is manifest as viscoelastic properties. On short timescales the fibrils react elastically with a shear modulus
proportional to their overall magnetic energy density. On longer timescales they produce an effective viscosity
resulting from collective aerodynamic drag. The viscosity due to flux tubes in the solar convection zone can
be comparable to that attributed to turbulence there. These forces might have observable effects on the
convection zone flows
