A theoretical and numerical model is developed to describe the growth of Saccharomyces cerevisiae yeasts. This kind of cells is considered here as an axisymmetrical and deformable structure, the inner surface of which is continuously acted upon by a high turgor pressure. Due to the small ratio between the cell-wall thickness and the cell radius, a structural shell approach is used. Moreover, the finite strain range is assumed because of the soft nature of these cells. The adopted kinematics is herein based on the multiplicative decomposition of the deformation gradient into an elastic part Fe and an irreversible part related to the growth Fg, i.e. F = FeFg. The reversible response is described using an hyperelastic model of the Ogden type. Within the thermodynamics of continuum mechanics, a criterion is introduced to control the evolution of the growth phenomenon. In this latter two parameters are involved : a growth stress-threshold, and a growth characterstic time. Embedded within the finite element framework, an illustrative exemple shows the growth phenomenon of spherical cells going from yeast bud emergence to the step just before cell division. A parametric study highlights the influence of the stress-threshold and the characteristic time on the cell responses.