Heavy Flavor Production at the Tevatron

Using a subset of the current Run II data, the CDF and \D0 have performed several measurements on heavy flavor production. In this paper, we present a new measurement of prompt charm meson production by CDF. We also report the latest CDF II measurements of inclusive $J/\Psi$ production and $b$-production without requirement of minimum transverse momentum on $J/\Psi$ and $b$-quark. They are the first measurements of the total inclusive $J/\Psi$ and $b$ quark cross section in the central rapidity region at a hadron collider. The results of $J/\Psi$ cross section as a function of rapidity, and $b$-jet production cross section measured by \D0 are also reviewed