In this paper, stochastic planar stick-slip motions are investigated using a slider-on-belt model where the coefficient of friction (COF) of the contact interface is modelled as a random field. New three-variable stick-slip transition criteria are proposed to improve the accuracy and robustness of the algorithm. Stochastic analyses are performed concerning the Peak-to-Valley value of the displacement and friction forces and the time duration of the stick state. It is found that the correlation length of the COF random field is dominantly responsible for the stochastic behaviours of the system. In contrast, the belt velocity and the mean value of the COF have a significant influence on the time duration of the stick state compared with the corresponding deterministic slider-on-belt model.