The work is devoted to studying the influence of the bubble shell anisotropy on its radial oscillations near an elastic wall of finite thickness under the action of an external acoustic disturbance. For this purpose, a system of two equations that determine the pulsations of a gas bubble covered with an anisotropic shell of finite thickness is obtained. In the case when the thickness of the bubble shell is sufficiently small, which corresponds to most known ultrasound contrast agents, the system of equations is reduced to a single modified Rayleigh – Plesset equation. A generalization of this equation for the case of oscillations of an encapsulated bubble near an elastic wall is presented. A numerical solution of the obtained equation is carried out. The influence of the shell anisotropy and the presence of an elastic wall on the radial oscillations of a covered gas bubble in an external acoustic field is analyzed. In a particular case, a comparison of the theory with experimental data available in literature is given.