A theory of spin injection across a ballistic semiconductor embedded between two ferromagnetic leads is developed for the Boltzmann regime. Spin injection coefficient ␥ is suppressed by the Sharvin resistance of the semiconductor r N *ϭ(h/e 2 )( 2 /S N ), where S N is the Fermi-surface cross section. It competes with the diffusion resistances of the ferromagnets r F , and ␥ is small, ␥ϳr F /r N *Ӷ1, in the absence of contact barriers. Efficient spin injection can be ensured by contact barriers. Explicit formulas for the junction resistance and the spin-valve effect are presented.

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