In this study, we investigated the current saturation which forces the apparent resistivity to converge when the conductivity contrast between the anomalous body and background medium is greater than a specific value. Analizing theoretical and numerical solutions for some simple models, we studied the behavior of the surface charge, and how the surface charge cause the current saturation and finally lead to the convergence of the apparent resistivity in the resistivity method. As a consequence of above analysis, we verified that the current saturation makes the apparent resistivity converge to a specific value and the magnitude of the apparent resistivity anomaly be less than that of the ideal conductor or insulator in the resistivity method. In general, current saturation is considered to occur when the conductivity contrast becomes larger than 100.