The present article is focused on investigating the influence of process parameters under compressive loading in case of reentrant auxetic structures fabricated by fused deposition modeling (FDM). Auxetic structures of acrylonitrile butadiene styrene (ABS) and poly-lactic acid (PLA) materials are fabricated. Three process parameters of FDM namely layer thickness, raster angle, and number of contours are considered to investigate their influence on compressive strength, stiffness, and specific energy absorption (SEA). Experiments are performed on the basis of central composite design and analysis is performed using ANOVA. It is found that compressive strength of auxetic structure improves with increase in layer thickness. But with increase in raster angle, it increases first and then decreases. Compressive stiffness of structures initially decreases and then increases with increase in raster angle, while it increases with increase in number of contours. SEA of structures increases with decrease in layer thickness. Based on the analysis of experimental results, regression models are developed to predict these responses. Also, multi-response optimization is performed to optimize strength, stiffness, and SEA. Auxetic structures failed under compressive loading are also examined using scanning electron microscope.