Consider a manifold \(M\), a codimension one-submanifold \(\Sigma\) and a vector field \(X\) on \(M\), all three smooth or analytic. Given \(p\in \Sigma\), there exist a neighborhood \(U_p\subset M\) of \(p\) and a smooth or analytic function \(h:U_p\rightarrow \mathbb{R}\) such that \(\Sigma \cap U_p=h^{-1}(0)\) and \(\nabla h(x)\neq 0\) for \(x\in \Sigma \cap U_p\). By definition \(p\) is a \(k\)-contact between \(X\) and \(\Sigma\) if \(0\) is a root of multiplicity \(k+1\) for \(h\circ X_t(p)\), where \(X_t(p)\) is the trajectory of \(X\) starting at \(p\). Vishik’s normal form provides a local smooth conjugation with a linear vector field for a smooth vector field near a \(k\)-contact with a manifold. The authors focus on the analytic case and show that for analytic vector fields and manifolds, the conjugation with Vishik’s normal form is also analytic. As an application, they investigate the analyticity of Poincaré half maps defined locally near \(k\)-contacts between analytic vector fields and manifolds.