We present a model to describe electrical injection of spin polarized electrons and holes from ferromagnetic contacts into a conjugated organic semiconductor. Transport in the semiconductor is treated by the spin dependent continuity equations coupled with Poisson's equation. The recombination of injected electrons and holes is modeled as a Langevin process. The boundary conditions used to solve the continuity equations are formulated in terms of spin polarized particle currents at the boundaries. Injected spin currents are related to the charge currents via the transport parameters of the ferromagnetic contacts. Spin injection strongly depends on the contact polarization and the conductivity of the contact material. No approximations that limit the model to small current polarizations are made. In the case of conventional ferromagnetic metal contacts, the relatively weak polarization and high conductivity hinder spin polarized injection. Spin injection can be greatly enhanced if (spin dependent) tunneling is the limiting process, which may be described by spin dependent contact resistances. The dependence of the current polarization on these contact resistances is explored. On the other hand, if the injecting contacts are made from half-metallic materials with low conductivity, spin injection is strong even for thermionic injection and the spin current approaches the charge current.