Scheduling-Location (ScheLoc) problem is a new and interesting topic in manufacturing, considering location and scheduling decisions simultaneously. Most existing works focus on the deterministic problems. In practice, however, job-processing times are usually uncertain due to some factors. This paper investigates the stochastic parallel machine ScheLoc problem to minimise the weighted sum of the location cost and the expectation of the total completion time. A two-stage stochastic programming formulation is proposed, then the sample average approximation (SAA) method is adapted to solve the small-size problems. To efficiently address the large-scale problems, a genetic algorithm (GA) and a scenario-based heuristic are designed. Numerical experiments on 450 instances are conducted. Computational results show that the scenario-based heuristic outperforms SAA method and GA in terms of solution quality and computational time.