The increasing demand for Electric Vehicle (EV) charging is putting pressure on the power grids and capacities of charging stations. This work focuses on how to use indirect control through price signals to level out the load curve in order to avoid the power consumption from exceeding these capacities. We propose mathematical programming models for the indirect control of EV charging that aim at finding an optimal set of price signals to be sent to the drivers based on price elasticities. The objective is to satisfy the demand for a given price structure, or minimize the curtailment of loads, when there is a shortage of capacity. The key contribution is the use of elasticity matrices through which it is possible to estimate the EV drivers’ reactions to the price signals. As real-world data on relating the elasticity values to the EV driver’s behaviour are currently non-existent, we concentrate on sensitivity analysis to test how different assumptions on elasticities affect the optimal price structure. In particular, we study how market segments of drivers with different elasticities may affect the ability of the operator to both handle a capacity problem and properly satisfy the charging needs.