The Snowball Earth theory initially proposed by Kirschvink (1992) to explain the Neoproterozoic glacial episodes, suggested that the Earth was fully ice-covered at 720 Ma (Sturtian episode) and 640 Ma (Marinoan episode). This succession of extreme climatic crises induced environmental perturbations which are considered as a strong selective pressure on the evolution of life (Hoffman et al., 1998). Using a numerical model of carbon-alkalinity global cycles, we quantify environmental stresses caused by a global glaciation. According to our results, we suggest that during global glaciations, the ocean becomes acidic (pH~6), and undersaturated with respect to carbonate minerals. Moreover the quick transition from ice-house to greenhouse conditions implies an abrupt and large shift of the oceanic surface temperature which causes an extended hypoxia. The intense continental weathering, in the aftermath of the glaciation, deeply affects the seawater composition inducing rapid changes in terms of pH and alkalinity. We also propose a new timing for post glacial perturbations and for the cap carbonates deposition, ~2 Myr instead of 200 kyr as suggested in a previous modelling study. In terms of Precambrian life sustainability, seawater pH modifications appear drastic all along the glaciation, but we suggest that the buffering action of the oceanic crust dissolution avoids a total collapse of biological productivity. But short-lived and large post-glacial perturbations are more critical and may have played the role of an environmental filter proposed in the classic snowball Earth theory. Although the link between environmental changes and life sustainability cannot be modelled accurately, we suggest that only a permissive life (Knoll, 2003) may explain the relative continuity in microfossils diversity observed before, during and after Neoproterozoic glaciation events.