A theoretical examination of the behavior of bubbles in non-Newtonian fluids is made by using a Carreau model which is said to represent the rheological behavior in problems of engineering with sufficient accuracy. The equation of motion for a bubble and the pressure equation are obtained, and then examples of numerical calculations are shown for the cases of various polymer solutions and an aluminum soap solution. Consequently, when the initial bubble radius is small, it is found that the damping effect on the bubble oscillation becomes strong, and that the maximum pressure p//m//a//x occurring during the bubble collapse becomes small.