We report on observations of very high-energy \gamma rays from the shell-type supernova remnant Cassiopeia A with the VERITAS stereoscopic array of four imaging atmospheric Cherenkov telescopes in Arizona .
The total exposure time for these observations is 22Â hours , accumulated between September and November of 2007 .
The \gamma -ray source associated with the SNR Cassiopeia A was detected above 200 GeV with a statistical significance of 8.3 \sigma .
The estimated integral flux for this \gamma -ray source is about 3 % of the Crab-Nebula flux .
The photon spectrum is compatible with a power law dN / dE \propto E ^ { - \Gamma } with an index \Gamma = 2.61 \pm 0.24 _ { stat } \pm 0.2 _ { sys } .
The data are consistent with a point-like source .
We provide a detailed description of the analysis results , and discuss physical mechanisms that may be responsible for the observed \gamma -ray emission .