Additive Manufacturing (AM) techniques are increasingly being adopted in the construction industry to accelerate and automate the construction process, while also offering new architectural possibilities and reducing waste. Among AM techniques, 3D Concrete Printing (3DCP) is the most widespread for cementitious-based construction applications. In 3DCP arbitrarily shaped objects and structural components are created by filament deposition of a cementitious mortar through a digitally controlled nozzle. However, due to the limited understanding of how the printing process affects the material and structural performance, there is still a lack of standardization and regulation of this technology. The development of reliable computational tools, able to simulate and optimize the printing process, would represent a great leap forward for the diffusion and large-scale adoption of 3DCP. In this work, an original numerical model for the simulation of the printing process of cementitious materials is presented. The model is based on the single-phase fluid assumption and the governing Navier-Stokes equations are solved with the Particle Finite Element Method (PFEM) [1] to cope with the large distortions of the computational domain. It is further discussed how to impose a time-varying moving boundary condition at the nozzle outlet and how to improve interlayer contact in the PFEM framework. As the computational cost is one of the main challenges faced in 3DCP simulations, the use of an adaptive de-refinement technique is also introduced. The results obtained by applying the model to different printing scenarios are compared with the experimental data [2,3] and show a very good agreement. Concluding, the developed numerical model can reliably simulate the extrusion and layer deposition phases of 3DCP. Moreover, it could be extended in the future to simulate longer printing processes, accounting for different phenomena, such as thixotropy and the fluid-to-solid phase transition due to the hydration reaction of cement.