The compressive and flexural strengths of mortars modified with ethylene-vinyl acetate (EVA) were experimentally investigated for use in three-dimensional (3D) additive construction (3DAC). EVA powder, which is available in a premix type, was employed as an admixture. The test results for the cast specimens showed that, at a curing age of 28 days, the compressive strengths ranged from 32.92 MPa to 43.50 MPa, and the flexural strengths ranged from 12.73 MPa to 14.49 MPa. The compressive and flexural strengths of the printed specimens were relatively lower: 23% to 26% and 3% to 7%, respectively. The compressive strength also decreased and the flexural strength increased when the EVA/cement ratio was increased. The results of the experiment reveal that the EVA-modified mortar had a high rate of strength development early on, making the material advantageous for use in 3DAC. It was determined that the appropriate EVA/cement ratio ranged between 5% and 15%. However, the printed specimens exhibited lower compressive and flexural strengths than did the cast specimens, and the compressive strength decreased as the EVA content was increased. This study provides the compressive and flexural strengths of common EVA-modified mortars, important data for 3DAC applications.