Microenvironmentally restricted yeast cell growth within Ca-alginate beads with and without entrapped gas bubbles was considered based on experimental data. Cell growth dynamics was described by (1) the dimensionless cell number density as a function of the cell growth time and (2) the cell distribution per bead cross sections. One of the key control parameters for bioprocess optimization is the matrix resistance stress generated during immobilized cell expansion. The dynamics of the increase in matrix stress was described theoretically based on a multi-scale mathematical model. In order to estimate and reduce the accumulation of matrix stress we considered repeated stress relaxation cycles in separate rheological experiments without immobilized cells. The results revealed that the increase in resistance stress within the Ca-alginate matrix was significant (similar to 7 kPa) after 10 repeated cycles, even under a low compression strain of 2% per cycle. The stress could be reduced by using the Ca-alginate matrix with entrapped gas bubbles. The final cell concentration within the beads with entrapped bubbles was 3.3 times higher in comparison with the beads without bubbles. The bubbles could locally amortize the compression effects within the surrounding cell clusters. (C) 2016 Elsevier Ltd. All rights reserved.