A general scattering problem of a plane electromagnetic wave on an infinite cylindrical rod is formulated and solved in a form of Bessel functions series expansion. The conductivity account via Ohm law directly in Maxwell equation leads to complex wavenumber and hence the complex arguments of Bessel functions inside the cylinder. The general formula for averaged by period Pointing vector is derived. For numerical calculations asymptotics of Bessel functions are used. Dependence of scattered wave intensity as function of angle and frequency is presented for different values of the rod radius.