Concentrating solar power plants are an attractive option in the renewable energy generation market. The possibility of integrating relatively cheap forms of energy storage makes them a desirable solution when power generation must be readily available at any time of the day. Solar power plants typically start-up and shut down every day, so in order to maximize their profitability, it is necessary to increase their flexibility in transient operation and to initiate power generation as rapidly as possible. Two of the key components are the steam generator and steam turbine and the rates at which they can reach operational speed are limited by thermomechanical constraints. This paper presents an analysis of the effects of the thermal stress limitations of the steam generator and steam turbine on the power plant start-up, and quantifies their impact on the economy of the system. A dynamic model of a parabolic trough power plant was developed and integrated with a logic controller to identify start-up limitations, and subsequently the dynamic model was integrated in a technoeconomic tool previously developed by the authors. The plant was analysed under two different operating strategies, namely solar-driven and peak-load. The results indicate that for steam generator hot start-ups, a 1.5% increase in peak-load electricity production would be achieved by doubling the maximum allowable heating rate of the evaporator. No useful increase would be achieved by increasing the rates beyond a limit of 7-8 K/min, as the turbine would then be the main limiting component during start-up. Similar conclusions can be drawn for the solar-driven case, for which the solar field and the energy source availability would pose the major constraint when starting up the steam generator system.