We compute within the effective-mass theory and without adjustable parameters the Stark effect for shallow P donors in Si with anisotropic band structure. Valley-orbit coupling is taken into account in a nonperturbative way and scattering effects of the impurity core are included to properly describe low-lying impurity states. The ground-state energy slightly decreases with increasing electric field up to a critical value E cr∼ 25 keV∕ cm, at which the donor can be ionized by tunneling due to a field-induced mixing of the “1 s-like” singlet ground state with a “2 p 0-like” excited state in zero field. The resulting ground-state wave function at high field extends significantly outside the potential barrier surrounding the impurity. Calculations of the hyperfine splitting and of the A-shell superhyperfine coupling constants as a function of the electric field complete the work.