Not yet reviewed by Pith; the record is open.

We study collisions of ultracold CaF molecules in strong static electric fields. These fields allow the creation of long-range barriers in the interaction potential, effectively preventing the molecules from reaching the short-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channel calculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for including energetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show that shielding is particularly efficient for CaF and allows the rate of two-body loss processes to be reduced by a factor of $10^7$ or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron and nuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. These results pave the way for evaporative cooling of CaF towards quantum degeneracy.