This work examines the identification of defects in anisotropic laminated composite structures using the boundary element method (BEM) from incomplete static response data including noise effects. The main objective in this paper is to anticipate effects of layup sequences and sensitivity of a measurement system of two-dimensional structures made of composite materials for detecting defects. It is a key goal to create understanding on the influence of the monitorization of advanced structures into their design. The identifiability is studied in terms of layup, measurement and loading design by using boundary element modeling. The concept of identifiability is based on the existing inversion strategy, which consists of the minimization of a cost functional with the possibility of taking into account the entire measurement-specimen system, and therefore interpreting quantitatively the measurements. In this article, after verifying that the boundary element model is in good agreement with numerical results reported by other investigators, the effect of noise in the measurements on the identifiability is studied with respect to different design parameters of laminated composites using a wide set of numerical examples.