Mass conservation is a key issue for accurate streamline construction. We introduce a mass conservative streamline tracking method using dual stream functions over tetrahedral domains. A set of exact dual stream function solutions for mass conservative linear momentum vectors have been evaluated and are presented here together with their computer graphics renderings. The local behavior of streamlines is described by stream function maps which display the transformed tetrahedra in a two-dimensional "mass flux space," where all streamlines are normal to the plane of the map. The map can be used to determine how faces of a tetrahedron are connected by the streamlines. The mass conservative streamline tracking method uses the intersections of the exact dual stream functions as the streamline segments in tetrahedra and connects the segments to generate streamlines in the domain of the velocity fields. The method can be used to draw streamlines for the velocity fields of steady flows given at discrete locations in three dimensions.