Vortex-induced vibration of a circular cylinder is a major research topic due to the immense applications they have in daily and industrial scenarios. Large numbers of studies have been conducted in this area in numerical and experimental domains with focus on understanding the response types, understanding the range of lock-in, the flow behavior, etc. However, most of the studies till date have been done in a deterministic environment; on the pretext that all factors about the incoming flow and input parameters are exactly known. In real-time flows, there can be a significant amount of uncertainties associated with various system parameters, which are traditionally not taken into consideration for the system. For example, randomness associated with the incoming flow might have significant effect on the associated dynamics. In this study, we do a stochastic modeling on a circular cylinder exhibiting free vibrations with one and two degrees of freedom. For this, we use Duffing Van der Pol combined system and impose fluctuations at every time step in the input flow by modeling them through a uniform distribution. The transverse oscillations of each of the cases under the presence of noise are individually studied. It is seen that noise brings in new dynamical states to the cylinder response compared to the deterministic cases. It is observed that there is a considerable difference between the responses of the single degree of freedom and two-degree of freedom cylinder. These qualitative differences are investigated in detail in the current study. © 2021, Springer Nature Singapore Pte Ltd.