A computer simulation method was used to study the electrical pre-breakdown events in dielectric liquids. This study concentrated on the liquid-solid interface. The suitable model based on the cavitation theory. It was assumed that the streamer channels are weak plasmas and those channels have a high electrical resistance. The model was implemented numerically by finite element method (in two-dimensions). It was tested within a pin-plane configuration using the n-hexane and the water as dielectric liquids. Same voltage and electric field distributions were shown in the two liquids. But different distributions appeared when the solid insulator was introduced to the configuration. Also, the results show that, a strong dependence of the streamer growth path on the mismatch permittivity between the solid and the liquid. It was shown a nearest picture for the streamer behavior within the dielectric liquids. That can help the designers of the high voltage equipment.