Incipient faults are used to describe transient self-recovery faults that will not cause relay protection actions in the system. Fault prediction and early warning of distribution network faults can be realized based on incipient fault detection and identification. This is of significance for improving power supply reliability. Affected by the neutral grounding method, incipient faults in a non-solidly grounding system manifest in different ways. For the characteristics and operating requirements of such a system, this paper analyzes and summarizes manifestations and characteristics of grounded incipient faults quantitatively from the equivalent circuit and simulation modeling. Results indicate that grounded incipient faults are divided into single-phase-to-ground fault and two-point grounding fault in two phases, and characteristics of incipient fault waveforms are summarized. The conclusions are verified by simulation and field data, and will provide theory and data support for detection and identification of incipient faults in non-solidly grounding system, as well as fault prediction and early warning. This work is supported by the National Key Research and Development Program of China (No. 2020YFF0305800) and Sichuan Applied Basic Research Project (No. 2020YJ0012).