In this paper, a biological model made up of a multilayer elliptic cylinder is considered. This canonical scattering problem is solved by a recursive procedure, which has been generalized to the case of lossy materials by using the analytical properties of Mathieu functions. Although it is a simplified model, this stratified configuration may simulate better than circular cylinders the local behavior of biological subsystems. In addition, it represents an effective tool for producing analytical data for testing direct-scattering numerical codes in biomedical applications and for the evaluation of reconstruction procedures in medical imaging.