This research is motivated by the numerical modelling of ultrasonic non-destructive testing experiments. Some tested media feature thin layers which are difficult to handle in numerical computations due to the very small element size required for meshing them. To overcome these difficulties, one idea consists in using effective transmission conditions (ETCs) across the two interfaces bounding the layer. This work aims at establishing such ETCs by means of a formal asymptotic analysis with respect to the (small) layer thickness.