In the latest research, it has been proven that from the point of view of losses in a cable distribution line, the most advantageous operation is to work with two or one phase of metallic cable screen ungrounded. However, such an operation may cause changes in the network characteristics and thus the occurrence of undesirable phenomena. One of those characteristics is the overvoltages in those cable screens, which can lead to cable line damage. The simulation tests presented in this article are closely related to the unusual method of operation of the MV cable screens and their performance, and they address the question of whether in a given system ground fault overvoltages may be a significant threat to the operation of the cable. The research methods used to verify these risks are related to the simulation of the cable line operating states using the DIgSILENT PowerFactory program (DIgSILENT GmbH, Gomaringen, Germany). Overvoltage simulations were performed, taking into account changes in the network configuration, such as the method of cable screens grounding, the length of cable lines, the cross-section of the conductor and cable screen, or the method of operation of the neutral point. The results for the cable line modeled as a part of the MV network with the variables considered during the tests indicate the possible impact of the one-sidedly cable screen ungrounding on overvoltages in this cable screen. The obtained results at the level of a few kV in one-sidedly ungrounded cable screens show that the change of the configuration of the operation of these cable screens may affect the safety of the network operation.