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This paper presents a method for computing input admittance and transient voltage responses in axisymmetric multi-stage cascaded waveguides, excited by a phi-independent EM source. A set of coupled integral equations is derived to determine the fields in the waveguide apertures. The method of moments (MoM) and the equivalence principle are employed to enhance numerical analysis, with electric field integral equations (EFIE) and magnetic field integral equations (MFIE) together with connection algorithm formulated in the frequency domain. The transient responses of various multi-stage cascaded waveguides with multiple discontinuities are obtained through inverse FFT over wide frequency ranges.