A new CNC assisted pellet-based fused layer modeling (FLM) process has been presented. It allows the fabrication of highly flexible parts which is not easily possible through the fused filament fabrication (FFF) process as buckling occurs when the flexible filament is fed into liquefier head. Instead of the filament, the presented FLM process utilizes the material in pellet form. The FLM process is different from the other extrusion based AM processes and has its own characteristics. Therefore, the current paper presents a parametric investigation in the developed FLM process by considering the ethylene vinyl acetate (EVA) material. Experiments have been conducted using the ‘one factor at a time’ (OFAT) approach. The effects of barrel temperature, bed temperature, screw speed, deposition speed, standoff distance between nozzle and bed surface have been studied on the melt flow rate, layer thickness and road width. The obtained results showed that the melt flow rate of EVA is increased with the increase in the screw speed and barrel temperature. A significant variation of approximately 27% was observed in the layer thickness with the change in the deposition speed and standoff distance. A decrease of 42.42% was observed in the road width when the standoff distance was reduced from 2 to 0.8 mm. Based on the investigation, a set of suitable process parameters was obtained to fabricate the flexible parts of the EVA material. The outcomes of the current study showed that the developed FLM process has the capabilities of fabricating parts utilizing a set of suitable process parameters.