A proper numerical analysis of geotechnical problems dealing with soil excavation is a useful tool for design and interpretation of civil engineering projects. It allows the prediction of the variation of stress and strain fields induced by excavation and its impact on the surrounding environment. The procedure adopted to simulate soil excavation with MPM consists in defining the range of calculation steps in which the material points (MPs) belonging to a certain volume have to be removed, once the geometry and the computational mesh are created. In order to contribute to the evaluation of this feature, numerical analyses of two excavation problems are carried out. In the first example, the bottom heave stability of a supported excavation in clay is analysed. This stability problem has been widely investigated theoretically and numerically by using different approaches. A series of undrained total stress analyses with decreasing value of soil strength are performed until failure conditions are reached. The aim is to discuss capabilities and limitations of MPM in simulating this kind of problem and to compare the results with the literature. A second simulation refers to a well-documented real case of a large landslide reactivated by quarry excavation [6]. The actual response, which induced a few centimetres of run-out, is well reproduced by the MPM model.