Nature being so nonlinear provides substantial reasoning to study the nonlinear dynamics inherited by the systems. Almost all of the systems that exist are nonlinear and analysis of such type of systems is necessary to understand a certain phenomenon. This paper presents a qualitative analysis of a coupled van der Pol's oscillator with the study of limit cycles. In order to get an approximate analytical solution of coupled van der Pol's (CVDP) oscillator system, a well-known perturbation technique, Method of Multiple Scales (MMS), is used. Stability and periodic construction of the van der Pol's system is examined by means of Floquet Multipliers and Shooting Method. Eigenvalues of Monodromy Matrix, a by-product of shooting method, are analysed to distinguish between hyperbolic and non-hyperbolic solutions of the system.