This work presents the dynamic modeling of a vertical multi-effect evaporator plant designed and manufactured for its installation at a commercial concentrating solar power (CSP) plant, within the framework of EU H2020 project SOLWARIS (Solving Water Issues for CSP plants). The model has been developed using Modelica computational language and implemented in Dymola® software environment. The results from the validation show a good agreement against the design data, obtaining relative errors lower than 5%. The dynamic response of the plant against external disturbances of the motive steam mass flow rate, feedwater mass flow rate and condenser pressure has been investigated. The main results reveal that increasing the motive steam flow rate by 5% produces a similar increment of the water recovered (5.2%), although the concentrate salinity is raised to an unsafe operation zone (106%) that could lead to scaling issues in the evaporators. The same effect occurs when the feedwater is decreased by 5% from its nominal value, causing a significant rise in the concentrate salinity (163%). In those cases, the simultaneous and proportional variation of the motive steam and feedwater mass flow rates allows maintaining the outlet concentrate salinity far from scale formation limits.