In the present work, we aim at improving our understanding of the effect of synthetic flexible fibers on the rheology of fresh cement-based suspensions. We first measure the way that synthetic fibers do increase the yield stress of various fresh cement pastes and mortars. We then measure, using micro CT, the way these fibers are deformed in a fresh paste. Finally, we propose a simple physical model allowing for the prediction of the fibers conformation as a function of their geometry, their elastic properties and the rheology of the cement-based material, into which they are dispersed. We validate this model on our results and discuss its application at the scale of mortars and concretes.