We reduce the rigorously formulated problem of diffraction of a plane electromagnetic wave by a perfectly conducting cylindrical wedge with a rounded apex to solving the system of linear algebraic equations of the second kind for unknown coefficients of the Fourier expansions of the diffracted-field components. The expansion coefficients are determined analytically in the long-wavelength approximation. The results of calculations of the diffracted field in the far zone are presented with a given accuracy in the case of an E-polarized wave. It is shown that the rounding of the apex of a cylindrical wedge leads to an increase in the backscattering coefficient of the structure in the long-wavelength range.