The paper presents the equations and numerical solutions of oscillation of the bubble cavitation in the non-Newtonian viscous fluid and viscoelastic fluid. The properties of viscous liquid were described by the involution model and the viscoelastic properties by the OWF (Oldroyd-Walters-Fridrickson) model. The characteristics of oscillation of a single bubble cavitation obtained from the numerical calculations are different for the Newtonian and non-Newtonian liquids. From the numerical analysis it follows that the viscosity and elasticity of fluid significantly limit the cavitation effect. The characteristics of velocity and pressure oscillation show the reduction of vibration amplitude of a bubble along with the increasing viscosity and elasticity of fluid.