Theory has been developed to calculate microstreaming velocity inside and outside an isolated air bubble in a liquid produced by a bubble-scattered sound field, taking account of two predominant modes of the bubble's motion: a monopole (pulsation) and a dipole (translational harmonic vibrations). It has been demonstrated that streaming velocity inside a bubble is much greater than that outside the bubble. It has also been shown that the microstreaming is most pronounced for a bubble undergoing volume resonance, which is in agreement with Elder's experimental observations [S. A. Elder, J. Acoust. Soc. Am. 31, 54--64 (1959)]. If the viscosity of the gas medium in a bubble is neglected in theory, the results obtained agree qualitatively with Davidson and Riley's [B. J. Davidson and N. Riley, J. Sound Vib. 15, 217--233 (1971)].