The evolution kinetics of a bubble population driven by a uniform production of gas in a yield-stress fluid matrix is investigated in the context of the long time swelling of bitumen drums in which radioactive salts have been dispersed (salts suspensions in a bitumen matrix). Radioactivity generates uniform volume production of hydrogen by radiolysis of bitumen chains. Since the production rate of gas occurs on very long time scales (more than a hundred years), one needs to set up theoretical models to predict the material swelling. It has been shown in previous studies that bitumen is a yield stress fluid. Therefore, the present work proposes to study the influence of a yield stress and of the production rate of gas on the evolution kinetics of a bubbles population. Usually, in a non-yield stress fluid and without gas creation, a supersaturation of gas leads to a scenario of germination, bubble growth and Ostwald ripening (growth of large bubbles at the expense of smaller ones). Over long times, a self-similar distribution of large bubbles is selected, independent of the initial distribution of nuclei. In this work, it is shown that there exist conditions for which the yield stress competes with the kinetics of ripening and induces hysteresis phenomena on the kinetics of bubbles distribution. The coupled effect of gas production rate and yield stress on the final population is discussed. (C) 2016 Elsevier B.V. All rights reserved.