This paper describes theoretical calculations of the combined effect of bulk and interfacial rheological properties on dissolution behavior of a bubble in an infinite medium at saturated conditions. Either bulk or interfacial elasticity can stop the bubble dissolution process, and stability criteria are defined for the elastic cases. In the case of an elastic interface with dilation modulus E-d and a bubble with an initial radius R-0 and initial interfacial tension sigma (0), the bubble is stabilized as it has shrunk to a relative radius of epsilon = R/R-0 = exp(-sigma (0)/(2E(d))). In case of an elastic bulk with modulus G a bubble will shrink until GR(0) = 4 sigma (0)epsilon (3)/(1 - 5 epsilon (4) + 4 epsilon (3)) is fulfilled. Bulk and interfacial viscosity can retard the dissolution process if their magnitude exceeds a certain critical value but will never completely stop bubble dissolution.