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The critical behavior at the ordinary transition in semi-infinite n-componentanisotropic cubic models is investigated by applying the field theoreticapproach in d=3 dimensions up to the two-loop approximation. Numericalestimates of the resulting two-loop series expansions for the criticalexponents of the ordinary transition are computed by means of Pade resummationtechniques. For $n<n_{c}$ the system belongs to the universality class of theisotropic n-component model, while for $n>n_{c}$ the cubic fixed point becomesstable, where $n_{c}<3$ is the marginal spin dimensionality of the cubic model.The obtained results indicate that the surface critical behavior of thesemi-infinite systems with cubic anisotropy is characterized by a new set ofsurface critical exponents for $n>n_{c}$.Comment: 11 page

Surface critical behaviour of semi-infinite systems with cubic anisotropy at the ordinary transition