Abstract
In this paper, we derive some new invariant solutions of dark energy models in cylindrically symmetric space-time. To quantify the deviation of pressure from isotropy, we introduce three different time-dependent skewness parameters along the spatial directions. The matter source consists of dark energy which is minimally interacting with perfect fluid. We use the symmetry analysis method for solving the non-linear partial differential equations (NLPDEs), which is more powerful than the classical methods of solving NLPDEs. The geometrical and kinematical features of the models and the behaviour of the anisotropy of dark energy are examined in detail.