  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.
