Abstract <p>The appearance of chaos in the stack of Josephson junctions (JJ) with the capacitive and inductive coupling along the current-voltage characteristics (CVC) is studied. Numerical simulations of the CVC and chaos indicator, such as Lyapunov exponent are performed. It is found that the chaotic features are triggered by the moving fluxons and inductive coupling. We compare the results for a stack of junctions with the case of a single junction and discuss the origin of the observed chaos and the effect of coupling between the junctions. Our results provided a guide for specific parameter combinations that could minimize the chaos, thereby making certain applications potentially more viable. We also demonstrated the appearance of additional branches on the current-voltage characteristic due to the occurrence of different numbers of fluxons in each JJ of the stack. It makes possible to analyze the internal dynamics of the coupled JJ stack based on an experimental study of the current-voltage characteristic branches.</p>