Entry and exit flows through abrupt contractions are studied numerically for Casson fluids exhibiting a yield stress. The Casson constitutive equation recommended for describing blood flow is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of unyielded/yielded regions along with the swelling ratio of the free stream for planar and axisymmetric contraction flows for the whole range of Casson numbers. The results for pressure are used to determine the excess pressure losses that give rise to entrance, exit, and the total end correction.