The dynamic response and stability of a single‐degree‐of‐freedom structural system composed of a hollow or solid sphere connected by a massless supporting member and submerged in a viscous fluid medium is studied. The constitutive relationship between the connecting member and the base is considered to be of a generalized Maxwell model type. Basset's fluid reaction is included in the integro‐differential equation of motion and a closed‐form solution is obtained by means of Laplace transforms. Response curves illustrating the effect of each dimensionless parameter on the response of the system are presented, and a dynamic stability criterion based on the character of the solution is employed to develop a stability profile for the system. It is demonstrated that the dynamic response of the system is significantly influenced by the character of the surrounding fluid medium while the stability or instability of the structure is determined by the relative values of the load parameter and the stiffness‐coefficient ratio.