Abstract This paper presents a parametric study and approximate integral abutment bridge (IAB) response prediction models. IABs are complex structures due to the nonlinearity and uncertainties in bridge materials and soil boundaries. Current design specifications and guides do not provide clearly defined analysis methods; therefore, there is a need for easily implemented preliminary analysis and accurate two-dimensional (2D) analysis methods. Based on a calibrated, nonlinear, 2D numerical modeling methodology including backfill–abutment interaction, soil–pile interaction and critical construction joints, a parametric study of 243 analysis cases was performed, consistent with the AASHTO 75-year bridge life. Analyses were performed under thermal load and gradient, and backfill pressure with time-dependent effects of concrete creep and shrinkage and prestressing steel relaxation included. The parametric study considered five parameters: (1) thermal expansion coefficient, (2) bridge length, (3) backfill height, (4) backfill stiffness, and (5) pile soil stiffness. Each of the five parameters was evaluated at three distinct magnitudes to cover the normal range of bridge construction. The parametric study revealed that the thermal expansion coefficient, bridge length and pile soil stiffness significantly influence the IAB response as measured by: (1) girder axial force, (2) girder bending moment, (3) pile lateral force, (4) pile bending moment, and (5) pile head/abutment displacement. The influences of backfill height and backfill stiffness are not relatively significant. The study results provide practical, preliminary estimates of the bridge response and ranges for preliminary IAB design and analysis.