Abstract : A biomechanical model is proposed for the growth of the brown alga Ecto-carpus siliculosus. Featuring ramified uniseriate filaments, this alga has two modes of growth: apical growth and intercalary growth with branching. Apical growth occurs upon the mitosis of a young cell at one extremity and leads to a new tip cell followed by a cylindrical cell, whereas branching mainly occurs when a cylindrical cell becomes rounded and swells, forming a spherical cell. Given the continuous interplay between cell growth and swelling, a poroelastic model combining osmotic pressure and volumetric growth is considered for the whole cell, cytoplasm and cell wall. The model recovers the morphogenetic transformations of mature cells: transformation of a cylindrical shape into spherical shape with a volumetric increase, and then lateral branching. Our simulations show that the poro-elastic model, including the Mooney –Rivlin approach for hyper-elastic materials, can correctly reproduce the observations. In particular, branching appears to be a plasticity effect due to the high level of tension created after the increase in volume of mature cells.