Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using ultrasounds or magnetic resonance imaging. The main issue is to solve the inverse problem that consists in estimating the elastic properties inside the plaque from measured displacements. This study focuses on the identifiability of elastic parameters. An idealised plane strain Finite Element (FE) model is used.