A general theory is developed to determine the dynamic characteristics and stability of a gas cavity situated in viscoelastic liquids whose rheological state is described by the generalized model of the Kelvin or Maxwell type. The characteristic function of the bubble‐liquid system is obtained by the first‐order perturbation method, including the effects of surface tension, vapor pressure, and thermodynamic behavior of the gas confined in the cavity. The zeros of the characteristic function determine the types of bubble growth, bound on unbound. The Hurwitz (or Routh) stability is employed to determine the conditions for the onset of incipient cavitation. The applications of the theory are demonstrated in some liquids having simpler shear‐stress‐shear‐strain relationship.