We have succeeded in simultaneously trapping a fermion and boson isotope pair of ytterbium (Yb) in a far off-resonant trap (FORT). We have found evidence of elastic cross collisions between fermions and bosons, and performed a successful sympathetic cooling of the fermions. We could also enhance the loading of the fermions Yb-171 in the crossing region in a crossed FORT via cross collisions between the fermions Yb-171 and the bosons Yb-174.