Unparticles ($U$) interact weakly with particles. The direct signature of unparticles will be in the form of missing energy. We study constraints on unparticle interactions using totally invisible decay modes of $Z$, vector quarkonia $V$ and neutrino
s. The constraints on the unparticle interaction scale $Lambda_U$ are very sensitive to the dimension $d_U$ of the unparticles. From invisible $Z$ and $V$ decays, we find that with $d_U$ close to 1 for vector $U$, the unparticle scale $Lambda_U$ can be more than $10^4$ TeV, and for $d_U$ around 2, the scale can be lower than one TeV. From invisible neutrino decays, we find that if $d_U$ is close to 3/2, the scale can be more than the Planck mass, but with $d_U$ around 2 the scale can be as low as a few hundred GeV. We also study the possibility of using $V (Z)to gamma + U$ to constrain unparticle interactions, and find that present data give weak constraints.
