A comprehensive parametric study is conducted to investigate the structural performance of reinforced concrete (RC) three-sided culverts (TSCs) and the applied earth pressures. Nonlinear finite element models were established for a range of TSCs configurations and were validated using full-scale field measurements of three TSCs with spans of 7.3, 10.4, and 13.5 m. The parametric study covered a wide range of main design factors, including backfill height, installation method, backfill soil type and compaction level, and concrete compressive strength. The results demonstrated that embankment installation method resulted in slightly higher earth loads on the culvert top slab and sidewalls compared to trench installation method. The results revealed that vertical arching factors (VAFs) stipulated in the CHBDC (CSA, 2019) for B1 and B2 standard installations consistently overestimated the vertical earth pressure on the top slab. Therefore, the equation proposed by AASHTO (AASHTO LRFD, 2014) for evaluating VAFs was modified and proposed to evaluate vertical earth pressures for TSCs. It was found that culvert installation involving dumped soil or moderately compacted sidefill along with compacted backfill on the top slab significantly increased the vertical earth loads on the top slab, and adversely affected the structural performance of TSCs and their ultimate capacity. Therefore, these compaction scenarios should not be used in the construction of TSCs. The results also demonstrated that the predicted maximum backfill height at failure could increase by up to 50% when concrete with higher compressive strength (i.e., 60 MPa instead of 40 MPa) is used in manufacturing the RC TSCs. Finally, midspan vertical deflection limits are proposed to ensure that the crack width of the RC culvert satisfies the allowable limits considering soil-structure interaction effects.