Reflection cracking is one of the main distresses in hot-mix asphalt (HMA) overlays. It has been a serious concern since the early 20th century. Until now, only limited research has been performed to predict reflection cracking. Mechanistic-based models were calibrated to field data to produce a design process for predicting reflection cracks. Three cracking mechanisms (bending, shearing traffic stresses, and thermal stress) were taken into account to evaluate the rate of growth of the three increasing levels of distress severity (low, medium, and high). The cumulative damage done by all three cracking mechanisms is used to predict the number of days for the reflection crack to reach the surface of the overlay. The result of this calculation is calibrated to the observed field data (severity and extent), which has been fitted with an S-shaped curve. In the mechanistic computations, material properties and fracture-related stress intensity factors are generated using efficient artificial neural network algorithms. The axle load spectra were used to represent traffic stresses, and a new model of predicting pavement temperature was incorporated into the thermal stress model. The HMA overlay was over either asphalt pavement or jointed concrete pavement in all four major climatic zones. The results of this calculated mechanistic approach showed HMA's ability to efficiently reproduce field observations of the growth extent and severity of reflection cracking. The computer running time for a 20-year prediction of a typical overlay was between 1 and 4 min.