Almost paracontact and normal almost paracontact Finsler structures on a vector bundle are defined. Finding some conditions, integrability of these structures is studied. Moreover, we define paracontact metric, para- Sasakian and K-paracontact Finsler structures and study some properties of these structures. For a K-paracontact Finsler structure, we find vertical and horizontal flag curvatures. Then, defining the vertical φ-flag curvature, we prove that every locally symmetric para-Sasakian Finsler structure has a negative vertical φ-flag curvature. Finally, we define the horizontal and vertical Ricci tensors of a para-Sasakian Finsler structure and study some curvature properties of them.
