In this study, we defined "paste tensile strength" as a gravity-based parameter in the uniaxial tensile direction of the food pastes. The objective was to evaluate the paste tensile strength effect on the printability of a screw-based 3D printer. Twenty-one different pastes made of three different agricultural products (pumpkin, potato, and carrot) flakes with water added were extruded in a vertical downward line from a 2 mm-diameter syringe. Paste tensile strength was measured based on the weight or image of a fragment of the paste that fractured spontaneously under its weight, and determined to be in the range of 50-1,420 Pa. This property was, to a certain extent, correlated with the yield stress, consistency index, Young's modulus, hardness, and adherence. Stable 3D-printing was observed in the region where the weight-based paste tensile strength was approximately 500 +/- 150 Pa, independent of the type of food ingredient. It was indicated that the paste tensile strength acts on extrusion stability as a resistance force in the uniaxial tensile direction and contributes to shape stability in conjunction with yield stress. The paste tensile strength defined in this study is expected to serve as a novel evaluation index for screw-based 3D food printers.