The plasma channel has an internal dynamic effect on the breaking process of the geotechnical body. For the development of plasma channel of the geotechnical body after the lightning strikes, the stochastic probability model of the geotechnical body breakdown channel was constructed from the viewpoint of the electric breakdown. The electric field was calculated by the Laplace equation, and the development probability was calculated by introducing the fractal theory. Then the simulation diagram of the plasma channel trajectory was obtained. The fractal dimension was calculated by the box dimension method to reflect the development process of the plasma channel. The influence of soil resistivity, lightning current amplitude and internal voltage drop on the fractal dimension was analyzed. The results showed that the fractal dimension decreased as the soil resistivity increased. With the increase of lightning current amplitude, the fractal dimension gradually increased, and the change of fractal dimension was more significant when the resistivity of soil was smaller. As the voltage drop inside the soil increased, the fractal dimension gradually increased. In this paper, the development of plasma channels within the geotechnical body was visualized by means of the two-dimensional images, and the development of plasma channels within the geotechnical body was quantitatively described by using fractal geometric relations, which can help predict the development law of the damage process of the geotechnical body and facilitates the physical nature of the electric breakdown of the geotechnical body.