Abstract: To precisely evaluate the bearing capacity of distribution networks for electric vehicles (EVs) and thus ensure the secure operation of distribution networks, this paper proposes the definition of the available capacity (AC) of EV charging stations (EVCSs) and its evaluation method on the basis of the multi-parametric programming theory. The proposed method can efficiently and accurately visualize the AC boundaries of EVCSs with full consideration of the implicit coupling effects among multiple EVCSs and assists in the decision-making of distribution network scheduling. Firstly, according to the economic scheduling model of distribution networks and Karush-Kuhn-Tucker (KKT) conditions, the equivalent constraint sets of AC are formulated to represent the feasible space of AC and provide accurate boundary information for the scheduling. Next, the piecewise operational costs for different AC sub-space are derived to reflect the impact of charging power on the economic operation of distribution networks. Finally, simulations on the modified IEEE-33 bus system demonstrate the accuracy and effectiveness of the proposed evaluation model.