Complete equations below the lowest cut-off frequency of transverse magnetic type relating the high frequency electric field and magnetic field inside a metallic cylinder excited through a gap and an assumed field at the gap are developed. Curves are calculated based on the equations which can be used to estimate the relative field strength at different points inside the cylinder. Equivalent capacitance due to the energy storage in the cylinder can be calculated and used for estimating the resonant frequency of the associated cavity. The equations can be degenerated to an electrostatic form and used for electron optical calculations.