Abstract: In the present article substantial Mathematical technique namely LDM and modified LDM has been employed to find the analytical solution of system of NLPDEs. Reliability of these methods were examined by illustrating three examples viz. Drinfield Sokolov (DS) system, coupled Burger’s equation and Cauchy problem. Both the methods have many advantages, they converge expeditiously to the exact solution also they do not require linearization, discretization or perturbation. Result obtained by these methods affirms that proposed methods are easy, powerful and efficient technique to find solution of wide class of system on NLPDs.