Description of tire model development using the finite element (FE) method is presented. Three-dimensional tire-pavement contact stresses were predicted for braking, traction, and free rolling using the FE method. Measured load-deflection curves, contact area, and contact stresses were used for model outcome validation. Slide-velocity-dependent friction and accurate input regarding geometry and material properties were considered. The developed tire model, which helped in studying contact stresses variation in each direction, was used to explain the various phenomena taking place at the tire-pavement interface during straight-line rolling. The analysis matrix includes nine rolling conditions and various loads, tire inflation pressures, and speeds. Vertical contact stresses were not significantly affected by speed or slip ratio; however, contact stresses were greatly modified along the in-plane directions by rolling conditions. Analytical expressions were introduced to represent vertical and longitudinal contact stresses for full braking and full traction. Formulas are presented for low speed and full braking, which are relevant for roadway intersections design
