Invasive alien species are a growing threat for the environment and health. They also have a major economic impact, as they can damage many infrastructures. The Japanese knotweed (Fallopia japonica), present in North America, Northern and Central Europe as well as in Australia and New Zealand, is listed by the World Conservation Union as one of the world's worst invasive species. So far, most models have dealt with the knotweed invasion without management. This paper aims to provide a model able to study and predict the dynamics of a stand of Japanese knotweed taking into account mowing as a management technique. The model is stochastic and individual-based, which allows us to take into account the behaviour of individuals depending on their size and location, as well as individual stochasticity. We set plant dynamics parameters based on a calibration with field data and studied the influence of the initial population size, the mean number of mowing events a year and the management project duration on the mean area and mean number of crowns. The results provide the sets of parameters for which it is possible to obtain stand eradication, and the minimum duration of the management project necessary to achieve this.