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Thermal storage is essential to increase energy efficiency of thermal systems. Phase change materials (PCM) can store high energy densities in small temperature differences by changing their phase from solid to liquid. To ensure not only high storage densities, but also suitable output power, a heat exchanger (e.g. a fin-and-tubes heat exchanger) has to be designed. To optimise PCM storages with such devices, a simulation model is helpful. To this aim, a model for a fin-and-tubes heat exchanger filled with PCM was developed in COMSOL Multiphysics. As the main focus of the model is on the behaviour of the PCM in combination with the fins, this part was modelled in 3D. The specific heat capacity of the PCM was included as input file, based on measurements of the material carried out in differential scanning calorimeter (DSC). This provides exact representation of the PCM behaviour, which could be shown by simulating DSC-experiments. The pipe flow in the heat exchanger was simplified to 1D to shorten simulation time. Both components are coupled to each other. The model was validated with measurement data from two fin-and-tubes heat exchangers with PCM. The heat exchangers differ in dimensions and in the PCM used: one uses a sugar alcohol (D mannitol, Tm=166 °C) and the other one uses a paraffinic commercial PCM (Plus ICE A82, Tm=82 °C). Results of both validations show good accuracy. Additionally natural convection in the liquid phase of the PCM was modelled. For small fin distances it has a negligible influence, but it becomes important for larger ones depending on the PCM. This was shown by further simulations. Afterwards the model was used to optimize both fin-and-tubes heat exchangers with PCM. The model, validation and optimisation results will be presented in this paper.