In vitro transmesothelial migration assays of ovarian cancer cells, isolated oraggregated in multicellular spheroids, are reproduced deducing suitable Cellular PottsModels (CPM). We show that the simulations are in good agreement with the experimentalevidence and that the overall process is regulated by the activity of matrixmetalloproteinases (MMPs) and by the interplay of the adhesive properties of the cellswith the extracellular matrix and between cells, both of the same type and of differenttypes. In particular, the process depends on the ability of the cell to induce theloosening of cadherin-mediated junctions. Coherently with experiments, it is found thatsingle cell invasion is more conservative with a crucial role played by MMPs. A similarimportant role is played in cell spheroid invasion, which in comparison is moredisruptive. It achieves monofocal or multifocal characteristics according to the relativeadhesion affinity among cells or between them and the mesothelial layer.