In this paper we estimate the influence of static pressure on the efficiency of passive damping of vibrations of a circular cylindrical shell using an open piezoelectric ring connected to a passive electric circuit of different configurations. The mathematical formulation of the problem of the dynamic behavior of an electroelastic structure is based on the variational principle of virtual displacements, which is written in matrix form taking into account the prestressed non-deformed state caused by applied loads, and as well as the work done by external surface forces, inertial forces and external electric field to transfer the free charge. The resulting equation is supplemented by the equation for the electric circuit, which relates the voltage at the piezoelectric ring with the corresponding electric charge. The problem is solved in the framework of 3D formulation using the finite element method. As examples, we consider the serial RL- and resistive R-circuits. Their parameters providing the most effective damping of free vibrations in terms of their decay rate are determined by solving the optimization problem. The results obtained by numerical simulations are compared with the results calculated by the analytical formulas at different values of static pressure.