Abstract: The sectorial waveguide can be used as an element of high power microwave(HPM) cylindrically conformal slotted waveguide array antenna. In this paper, the field components for the domination mode in a sectorial waveguide are investigated. According to the practicality applied area, the field components of domination mode can be reasonably approximated. By the reciprocity theorem, the amplitudes of forward or backward scattered mode can be expressed by the transverse field components of waveguide and the field components in slot. By the transmission line theorem, the longitudinal shunt slot is equivalent to a shunt obstacle on a two-wire transmission line. According to the boundary condition, the resonant normalized conductance of the slot is expressed by the amplitudes of scattered domination mode. The radiation resistance of half wavelength slot is obtained from the complementary half wavelength dipole. The amplitudes of scattered domination mode are expressed by radiation power of slot. The analytic formula of the resonant conductance for longitudinal shunt slots cut in the curved broad face of the waveguide is derived with the parameters of offset angle from the center line, the width of slot, the wavelength and guide wavelength and the dimension of inner cavity of waveguide. An example is presented and the result obtained in the middle area of waveguide is satisfactory.