An increasing number of electric vehicles (EVs) are replacing gasoline vehicles in the automobile market due to the economic and environmental benefits. The high penetration of EVs is one of the main challenges in the future smart grid. As a result of EV charging, an excessive overloading is expected in different elements of the power system, especially at the distribution level. In this paper, we evaluate the impact of EVs on the distribution system under three loading conditions (light, intermediate, and full). For each case, we estimate the maximum number of EVs that can be charged simultaneously before reaching different system limitations, including the undervoltage, overcurrent, and transformer capacity limit. Finally, we use the 19-node distribution system to study these limitations under different loading conditions. The 19-node system is one of the typical distribution systems in Jordan. Our work estimates the upper limit of the possible EV penetration before reaching the system stability margins.