We give Gysin formulas for all flag bundles of types A, B, C, D. The formulas (and also the proofs) involve only the Segre classes of the original vector bundles and characteristic classes of universal bundles. As an application  we provide new determinantal formulas. We also establish Gysin  formulas for Kempf-Laksov bundles and their isotropic analogs. This is a joint work with Lionel Darondeau.