Today, the use of asphalt pavements in the world shows an ascending trend. Since rutting failure is among the most common failures on roads, laboratory information is required to evaluate the potential of rutting. The static creep test has been used to evaluate the rutting susceptibility of asphalt mixtures for a long time. Evaluating the strains created in asphalt mixtures at different loading times and temperatures is among the most essential methods for modeling the visco-elastic behavior of asphalt mixtures. In addition, mechanical models have been used to evaluate the nonlinear viscoelastic behavior of asphalt mixtures. Some of these models include Burgers, Maxwell, generalized, and Kelvin models. In this research, the creep behavior of asphalt mixtures is evaluated over time using static creep tests at 2, 3, 4, and 5 bar at the controlled temperature of 40℃. Next, coefficients of determination (R²) for different mechanical models are determined to evaluate viscoelastic behavior. The experimental results and proposed mechanical models indicate that the Burgers model has the best performance (R² = 0.8) in predicting the viscoelastic behavior of asphalt mixtures at different pressures with a reliability of 95%. Finally, a logarithmic nonlinear viscoelastic model was proposed to predict the creep of asphalt mixtures by matching the experimental data.