Summary: We consider a two-form antisymmetric tensor field \(\varphi \) minimally coupled to a non-Abelian vector field with a field strength F. Canonical analysis suggests that a pseudoscalar mass term \(\frac {\mu^2}{2} \text{Tr}(\phi \wedge \phi)\) for the tensor field eliminates degrees of freedom associated with this field. Explicit one-loop calculations show that an additional coupling \(m \text{Tr}(\varphi \land F)\) (which can be eliminated classically by a tensor field shift) reintroduces tensor field degrees of freedom. We attribute this to the lack of the renormalizability in our vector-tensor model. We also explore a vector-tensor model with a tensor field scalar mass term \(\frac {\mu^2}{2} \text{Tr}(\phi \wedge \star \phi)\) and coupling \(m \text{Tr}(\varphi \land \bigstar F)\). We comment on the Stueckelberg mechanism for mass generation in the Abelian version of the latter model.