Culverts are often required under earth embankment to allow for the crossing of a watercourse, like streams, to prevent the road embankment from obstructing the natural waterway. The opening of the culvert is determined based on the waterway required to accommodate the design flood, whereas the thickness of the culvert section is designed based on the loads applied to the culvert. This paper studies some design parameters of box culverts, such as the thickness of the haunch, the coefficient of earth pressure, the thickness of box culvert, and depth of fill on the top slab, to show the effect of haunch on the stresses of the box culvert. The study investigated the variation in stresses and the cost comparison made for different width of the box culvert. The percentage reduction in the cost of culvert based on the presence of haunch is presented.