  The critical behavior at the ordinary transition in semi-infinite n-component
anisotropic cubic models is investigated by applying the field theoretic
approach in d=3 dimensions up to the two-loop approximation. Numerical
estimates of the resulting two-loop series expansions for the critical
exponents of the ordinary transition are computed by means of Pade resummation
techniques. For $n<n_{c}$ the system belongs to the universality class of the
isotropic n-component model, while for $n>n_{c}$ the cubic fixed point becomes
stable, where $n_{c}<3$ is the marginal spin dimensionality of the cubic model.
The obtained results indicate that the surface critical behavior of the
semi-infinite systems with cubic anisotropy is characterized by a new set of
surface critical exponents for $n>n_{c}$.
