The channel of a lightning stroke is modeled by an extremely elongated prolate spheroid of moderate electric conductivity. The model simulates return strokes if the center of the spheroid has electrical contact to an electric wall (the earth's surface). Otherwise, it simulates K strokes. Discharging of an electric charge within such spheroid occurs in an impulsive way due to the wave guide characteristics of the channel. The eigenvalues, eigenfrequencies, and eigenfunctions of electromagnetic fields and currents inside and outside the channel are calculated. They are compared with corresponding values of a cylindrical model. The agreement is reasonable as long as ∣ αl/c∣ ≦ 3, with α being the eigenfrequency, 2l being the channel length, and c being the speed of light. Most observed wave forms of return stroke currents and of sferics from return strokes or K strokes meet that condition.