In vitro transmesothelial migration assays of ovarian cancer cells, isolated or aggregated in multicellular spheroids, are reproduced deducing suitable Cellular Potts Models (CPM). We show that the simulations are in good agreement with the experimental evidence and that the overall process is regulated by the activity of matrix metalloproteinases (MMPs) and by the interplay of the adhesive properties of the cells with the extracellular matrix and between cells, both of the same type and of different types. In particular, the process depends on the ability of the cell to induce the loosening of cadherin-mediated junctions. Coherently with experiments, it is found that single cell invasion is more conservative with a crucial role played by MMPs. A similar important role is played in cell spheroid invasion, which in comparison is more disruptive. It achieves monofocal or multifocal characteristics according to the relative adhesion affinity among cells or between them and the mesothelial layer.