Using the data samples collected with the CDF Run II detector
during 2002 and early 2003, new measurements of the production cross
sections of charm and beauty hadrons at sqrt s = 1960 GeV are presented.
New measurements of the cross sections of centrally produced b-hadrons and
J/psi mesons down to zero transverse momenta have been carried out.  The
large charm signals made available by the silicon vertex track trigger have
enabled the measurement of the cross sections of D^0, D^*, D^+/-, and D_s
mesons.