© 2017 IEEE. Device modelling is a key enabling capability for the semiconductor industry, especially for process optimisation, and for insight into the physics of novel architectures and materials that are difficult to access experimentally. Despite much innovative experimental work, device modelling capabilities for field effect devices based on Transition Metal Dichalcogenide (TMD) channel materials are at an early stage of development. Properly formulated physics-based models would give a substantial improvement for time- A nd cost-effective development of TMD devices. In this work, experimental device data was used to develop models and parameter sets in the continuum-based Synopsys Sentaurus Device software. Specifically, few-layer MoS2 Field-Effect-Transistors (FETs) were systematically electrically characterized, and the modelling of the experimental data focused on the impact of impurities, interface traps, and contact barriers. Furthermore, the experimental MoS2 FETs device characteristics, combined with the physics based transport models, suggests that the low experimental electron mobility values are a result of a high density of charge impurity defects in the MoS2 channel. To the best of our knowledge continuum-based TCAD device models did not previously exist for MoS2, or TMD-semiconductors in general.