  In this paper, we address the problem of capacitated facility location
problem with penalties (CapFLPP) paid per unit of unserved demand. In case of
uncapacitated FLP with penalties demands of a client are either entirely met or
are entirely rejected and penalty is paid. In the uncapacitated case, there is
no reason to serve a client partially. Whereas, in case of CapFLPP, it may be
beneficial to serve a client partially instead of not serving at all and, pay
the penalty for the unmet demand. Charikar et. al.
\cite{charikar2001algorithms}, Jain et. al. \cite{jain2003greedy} and Xu- Xu
\cite{xu2009improved} gave $3$, $2$ and $1.8526$ approximation, respectively,
for the uncapacitated case . We present $(5.83 + \epsilon)$ factor for the case
of uniform capacities and $(8.532 + \epsilon)$ factor for non-uniform
capacities.
