In the context of electromagnetic wave propagation, we wish to adress the scattering problem from perfectly conducting thin wires. For numerical simulations, assuming their thickness to be much smaller than the wavelength of the incident field, it is not possible to take these obstacles into account without encountering problems of numerical locking. The Holland model (cf. \cite{Hol}), widely used in finite difference schemes, provides a pragmatic solution to this problem, by modifying the numerical scheme on vertices located in the neighbourhood of the wires. So far this model has not received any real theoretical justification, and involves a parameter, named lineic inductance, which is to be chosen on the basis of heuristic considerations. We are interested in the simplified problem of a bidimensional acoustic wave propagation in a medium including a small obstacle with homogeneous Dirichlet boundary condition. We present a numerical scheme suitable for finite elements that does not suffer from numerical locking, and takes the presence of the small obstacle into account. It is based on a combination between the fictitious domain method and matched asymptotic expansions. This results into a systematic generalization to the Holland model including an automatic computation of the lineic inductance. Our analysis leads to the first (to our knowledge) justification of this type of model. Even if we shall reduce our presentation to the 2D time harmonic case, it appears that this approach can be generalized to the 3D time dependent case (cf. \cite{Rogier},\cite{Fedoryuk},\cite{Art}).