In processes such as foam injection molding, due to the strong dependence of melt viscosity on gas content, the overall viscosity of a polymer melt will increase once the air phase (i.e., the bubbles) is developed in the polymer matrix. The diffusion of gas from the polymer melt into growing bubbles results in a gas concentration-dependent viscosity profile around each bubble, such that the viscosity at the bubble-melt interface can be significantly larger than further from the bubble. This effect of the viscosity profile on bubble growth and deformation is numerically investigated. We show that the viscosity variation slows the bubble growth rate at the early stages; this is more noticeable in low cell density foams. The effect of the viscosity profile on bubble deformation in a mold-filling simulation is also investigated. We show that the viscosity profile increases the resistance of bubbles to deformation, compared to bubbles that are assumed to be in a melt of uniform viscosity. This difference becomes more pronounced at larger capillary numbers. (c) 2019 The Society of Rheology.