Assuming the stochastic uncertainty in real-life decision making problems, this paper, we study mean-risk model for stochastic Unmanned Aerial Vehicles Surveillance Routing (SUAVsSRP) problem. We use the bi-objective formulation of this problem involving stochastic travel times, the model tries to optimize expected travel times and travel time reliability simultaneously. The risk value is chosen as the reliability measure. In order to deal with these complexities, we propose a simheuristic algorithm with two dominance criteria. It incorporates a monte carlo simulation (MCS), a stochastic dominance criteria, and a pareto metaheuristic. The role of MCS is an effective method to assess and calculate probabilistic objective functions, and theoretically, we focus on a concise overview of the variant concepts of univariate stochastic orders, and combining one of them with mean-risk pareto dominance to filter non-dominated solutions, note that, the choice between these order relations depends on the risk measures studied. The validity of this new simheuristic algorithm is studied empirically and the results demonstrate the ability of the proposed technique to generate a well-distributed set of mean-risk pareto-optimal solutions.