Shell thickness and infill density are key parameters for determining mechanical stability of a printed part when subjected to stress. This study aimed to establish models for predicting responses, specifically compressive strength, relative strength, and weight, and to analyze the interactive effects of both shell thickness and infill density on ABS prints, which were evaluated by conducting compression tests. For this purpose, the interactive effects of different shell thicknesses (0.4, 0.8, 1.2, 1.6, and 2.0 mm) and different infill densities (0%, 25%, 50%, 75%, and 100%) on the considered response variables, namely, compressive strength, relative strength, and material consumption of ABS prints were investigated. According to the results of the experiments, a specimen printed from ABS with a 75% infill density and a shell thickness of 2 mm has the highest relative compressive stress (1645 N/g). The evaluation of the effectiveness of the proposed prediction models was confirmed by comparing the measured data with the predicted data, which showed that the quadratic fit models presented in this study are suitable for all considered response variables. The model fits the data well, with a maximum error of 6.2%. By estimating the compressive strength, relative strength, and material consumption in relation to process parameters before manufacturing the FDM parts, the developed prediction models will assist practitioners in reducing the number of experimental works, resulting in material savings, reduced printing time, and reduced energy consumption.