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Tissue engineering's main objective is to create therapeutic constructs in vitro, capable to replace or remedy the functions of the tissue affected by different disease or totally destroyed. In order to obtain these constructs, the living cells are cultured on the different structure biomaterial. It has been shown that these constructs have properties which are similar to ones of human tissue, if the seeding is uniform. The paper presents a set of simulations of cell spreading on the plane surface of a biomaterial, based on the Metropolis Monte Carlo method. The model taken into account is formed of a cell aggregate placed on the planar surface of a parallelepipedic biomaterial. We study the influence of the cell-substrate and cell-medium interfacial tension parameters on the cell spreading process, analysing the number of cells attached to the biomaterial and the spreading rate of the cells. We also analyze the evolution of the centre of mass for the same value of cell-substrate interfacial tension and for different values of cell-medium interfacial tension. Experiments show an uniform and rapid cell spreading results if the cell-substrate and cell-medium interfacial tension have lower values.