The main objective of this work is to contribute to the valorization of plastic and glass waste in the improvement of concrete properties. Waste glass after grinding was used as a partial replacement of the cement with a percentage of 15%. The plastic waste was cut and introduced as fibers with 1% by the total volume of the mixture. Mechanical and durability tests were conducted for various mixtures of concrete as compressive and flexural strengths, water absorption, ultrasonic pulse velocity, and acid attack. Also, other in-depth analyses were performed on samples of each variant such as X-ray diffraction (XRD), thermogravimetric analysis (DSC-TGA), and scanning electron microscope (SEM). The results show that the addition of glass powder or plastic fibers or a combination of both in concrete improved in the compression and flexural strengths in the long term. The highest compressive strength was obtained in the mix which combines the two wastes about 26.72% of increase compared to the control concrete. The flexural strength increased in the mixture containing the glass powder. Therefore, the mixture with two wastes exhibits better resistance to aggressive sulfuric acid attack, and incorporating glass powder improves the ultrasonic pulse velocity.