Drilling fluids are essential for maintaining cutting suspension during drilling, exhibiting gel-like behavior at rest and liquid-like behavior under shearing. These fluids display shear-thinning behavior, yield stress, and thixotropy. This study investigates the impact of aging time on stress overshoot and the deformation required to disrupt the gelled structure of water-based and synthetic-based drilling fluids. Flow start-up tests were conducted using a rotational rheometer at 25 °C and atmospheric pressure. The results show that aging time significantly affects both stress overshoot and the shear strain needed to disrupt the gelled structure. Longer aging times reduce the strain required to break the structure, indicating a correlation between aging time and stress overshoot. The fitted model strongly correlates with the experimental data, providing valuable insights for the planning and simulation of offshore drilling wells, primarily in well stability.