Additive manufacturing (AM) is an emergent technology that witnessed significant growth demanded by the consumer market. One of the most used AM processes is the Fused Filament Fabrication (FFF) – an extrusion-based manufacturing process using fused thermoplastics. The FFF can build highly complex components and structures at a low cost. However, this additive technique is not extensively used in high-value industrial sectors mainly due to parts’ anisotropy, related to the deposition strategy, and residual stresses, caused by successive heating cycles. Thus, from the understatement of the major advantages and drawbacks of extrusion-based AM technologies, the process improvement and the optimization of the printed parts should be a matter of great interest in the research community – particularly in the numerical modelling and computational mechanics fields. In this work, an accurate and efficient meshless technique - the Radial Point Interpolation Method (RPIM) – is used to address the numerical simulation of the viscoplastic extrusion process, which is the initial phase of the FFF. Unlike the FEM, in meshless methods, there is no preestablished relationship between the nodes of the nodal mesh, and so the concept of ‘element’ is inexistent. Meshless methods, compared to the FEM, have shape functions with virtually a higher order, allowing a higher continuity and reproducibility. Moreover, the nodal discretization can be straightforwardly modified since nodes can be added or removed from the initial nodal mesh. Hence, meshless methods show a particular relevance if associated with AM processes since the nodes can be distributed to match the layer-by-layer growing condition of the printing process. Thus, using the flow formulation combined with the heat transfer formulation presented here for the first time within an in-house RPIM code, the proposed algorithm is developed, implemented, and then validated for benchmark examples. The accuracy of the obtained numerical results highlights the importance of using meshless techniques in this field.