Stochastic computing (SC), which is an approximate computation with probabilities, has attracted attention owing to its small area, small power consumption and high fault tolerance. In this paper, we focus on the transient fault tolerance of SC based on linear finite state machines (linear FSMs). We show that state assignment of FSMs considerably affects the fault tolerance of linear FSM-based SC circuits, and present a Markov model for representing the impact of the state assignment on the behavior of faulty FSMs and estimating the expected error significance of the faulty FSM-based SC circuits. Furthermore, we propose a heuristic algorithm for appropriate state assignment that can mitigate the influence of transient faults. Experimental analysis shows that the state assignment has an impact on the transient fault tolerance of linear FSM-based SC circuits and the proposed state assignment algorithm can achieve a quasi-optimal state assignment in terms of high fault tolerance.