The rheological model is developed to elucidate the mechanism of Ca-alginate microbead deformation in the course of cell growth within. It is a complex process influenced by relaxation of the expanded polymer network inside a bead, and forces generated by cell growth inside the bead and interactions between solvent, network parts and cells as well. The resulting effects are measured experimentally by estimating isotropic volumetric deformations of beads with yeast cells as function of time and cell concentration per bead. The mathematical model of the process is developed based on a modified general Zener model with fractional derivatives. It is particularly suitable for incorporating effects of different nature also during different stages of such complex process development. The results of theoretical analyses using the model developed and comparison with experimental values obtained, indicate a high impact of partial decomposition, i.e. plastic response of polymer network inside a bead due to cell growth, on bead deformation. For comparison, corresponding deformation measurements and modelling were performed on the same network system exposed to swelling in the solvent, but without the cells. In this case elastic forces are dominant, indicating different mechanism of relaxation without the influence of cells, in agreement with previous conclusions.