Current research was not dedicated to investigate the mechanical behavior of a concrete drainage pipe under multiphysical coupling conditions of overburden pressure, traffic loads, groundwater, and pipe fluids. This study proposes a new numerical solution method for coupled stress, seepage, and flow fields based on a validated finite element model. The model was developed by ABAQUS and FLUENT and then solved simultaneously using the MpCCI (mesh-based parallel-code coupling interface) platform. Results show that the tensile stress at the springline and the radial displacement at the crown (or invert) of the bell under the effect of groundwater alone were reduced by 50.5% and 38.1%, respectively, compared to the effect of traffic load alone. Parametric analyses show that vehicle speed and fluid height have a slight impact on the pipes. The soil cover depth, wheel pressure, and gasket strength are directly proportional to the pipe stress and vertical displacement. Within the scope of their respective changes, the pipe stresses were increased by 34.4%, 36.7%, and 28.5%, and the vertical displacements were increased by 124%, 95.85%, and 87.7%. The bedding and backfill strengths are proportional to the pipe stress and inversely proportional to the vertical displacement. Within the scope of their respective changes, the pipe stresses were increased by 18.2% and 20.0%, and the vertical displacements were decreased by 11.4% and 10.4%. Sensitivity analyses show that soil cover depth has a greatest impact on the pipe, followed by traffic load.