Background <p>The rolling friction, which exists between two objects with relative rotary motion that are familiar in engineering and in daily life, may induce significant unwanted vibration in mechanical systems. Compared with abundant studies on the friction induced vibration considering sliding frictional contacts, the study on the vibration induced by rolling frictional contacts has been scarce.</p> Purpose <p>To facilitate the dynamic analysis and evaluation of mechanical systems with parts undergoing non-smooth relative rolling, two representative dynamical models to explore the friction related vibration with rolling contacts are constructed and thoroughly investigated in this paper, namely, a single roller and a cyclic symmetric chain of rollers with frictional contacts with moving belt.</p> Methods <p>Three different numerical methods, i.e., one we propose for the friction induced vibration with rolling contacts, the smoothing method and the switch model method, are employed to calculate the transient dynamics of the rolling-frictional systems.</p> Results <p>The dynamic behaviours of the systems with rolling frictional contacts are in striking contrast with that with sliding frictional contacts. For the case of single roller, the bifurcations of the system responses with variations of key parameters are found. For the case of roller chain, the multi-stable responses in both situations of rolling frictional contacts and sliding frictional contacts are examined. Numerical results show much richer multi-stability phenomena in the situation of rolling frictional contacts than that in the situation of sliding frictional contacts.</p> Conclusions <p>Therefore, this work underlies the necessity to adopt rolling friction rather than sliding friction in the dynamic analysis and evaluation of mechanical systems with parts undergoing non-smooth relative rolling, e.g., shaft-bearing systems, pulley-belt systems, slider-rolling guide systems.</p>