The current design provisions for corrugated steel culverts in North America consider thrust at the springline to be the critical mechanism and location, respectively, when checking capacity. However, experiments have shown that, at shallow cover depths under vehicle loading, the response of these culverts involves both bending moments and thrust forces, and the critical location in terms of capacity is not at the springline. To address this, 3D finite element modeling of the culvert was undertaken using orthotropic shell elements for the corrugated steel structure and continuum elements for a discrete volume of the surrounding soil. The results of an extensive parametric study are used to develop equations for the critical thrust and bending moment under three different vehicle loading configurations. The proposed equations are then compared to the current design code equations in terms of how well they capture the behavior of the finite element model results. The proposed equations are then used to estimate the response of physical experiments conducted in the laboratory and the field and compared to the responses from distributed strain measurements. The equations were found to provide better estimates of thrust and allow the bending moments, which are currently not considered in North American design codes, to be estimated accurately. Limitations of the proposed equations are also discussed.