Rare decays of heavy flavor at the Tevatron

In this report I review recent results in the field of rare decays at the Tevatron CDF II and D0 experiments. The presentation is focused on rare decays of charm and bottom mesons with two muons in the final state. This includes improvements over the previously available limits on the following branching ratios: $B(D^+ \to \pi^+ \mu^+ \mu^-)< 4.7 \times 10^{-6}$, B(B_s^0 \to \phi \mu^+ \mu^-)< 3.2\times 10^{-6}$,$B(B_s^0 \to \mu^+ \mu^-)< 1 \times 10^{-7}$, and$B(B_d^0)< 3 \times 10{-8}$all at the 90$D_s^+ \to \phi \pi^+ \to \mu^+ \mu^- \pi^+$with a significance above background of over 7 standard deviations and evidence of$D^+ \to \phi \pi^+ \to \mu^+ \mu^- \pi^+$with a significance of 3.1 and$B(D^+ \to \phi \pi^+ \to \mu^+ \mu^- \pi^+)=(1.75 \pm0.7 \pm0.5) \times 10^{-6}$.