Eco-friendly recycled tire-derived rubberized concrete is an environmentally conscious alternative employed in civil engineering for diverse purposes, enhancing the characteristics of concrete. In this paper, the research focuses on examining the drying shrinkage, creep, impact, and postimpact and creep behavior of concrete incorporating rubber. Four groups of cylindrical samples, each with a diameter of 150 mm and a length of 300 mm, were subjected to a consistent load corresponding to 0.25 of the bearing load capacity determined through compression tests on identical concrete mixtures. The testing spanned a year, during which measurements were taken for total strain, dependent strain, creep, and shrinkage. The concrete mixtures were formulated with crumb rubber in place of fine aggregate sand, with varying percentages (0%, 10%, 20%, and 30%). To emphasize distinctions in outcomes across mixtures with different crumb rubber proportions, tests for compression, indirect tension, flexural strength, and impact resistance were carried out at intervals of 28 days, three months, six months, and one year. The examination and contrast of the four combinations demonstrated notable effects on both concrete creep and impact energy due to the addition of rubber particles. Despite this, shrinkage showed minimal influence. In general, there was a decrease in the compressive strength of rubberized concrete. The concrete compressive strength decreased by 25–35%, 45–50%, and 55–65% for rubberized concrete incorporating 10%, 20%, and 30% crumb rubber, respectively. Furthermore, it was observed that creep negatively affects the impact resistance of non-rubberized concrete. Nevertheless, including rubber helps mitigate the effect of creep on the impact resistance, resulting in a reduction ranging from 6% to 12% across rubber percentages from 10% to 30%.