An analysis is presented of the forced oscillations of a gas‐filled bubble at rest in a large body of a linear viscoelastic fluid. Two types of forcing are considered. In the first, oscillations are induced by a pressure surge on the system. For the three‐parameter fluid model employed, numerical computations show that for a given ratio of the fluid's elastic modulus to the pressure surge, the damping of the bubble motion exhibits a maximum as a function of the fluid relaxation time at a value of this parameter equal approximately to one‐fifth the natural period of oscillation. At very high or very low relaxation times, the damping becomes insignificant. As the second type of forced oscillation, we consider the motion induced by the application of ultrasonic waves to the system. Here, damping is found to depend strongly on the product of impressed frequency and fluid relaxation time.