This paper models linkages between upstream and downstream goods in the U.S. market for flat-rolled steel. These vertical linkages are important to account for when estimating the impact of trade restrictions on imports of flat rolled steel because some types of flat rolled steel are predominately used to produce other types of flat rolled steel and in some cases also make up a large share of their production costs. Previous research has modeled the linkages between upstream and downstream goods with CGE models and vertically linked partial equilibrium models. Drawing upon this literature, this paper builds a vertically linked version of the CES COMPAS model that incorporates vertical linkages as constant cross price elasticities in both downstream supply functions and upstream factor demand functions. Compared to estimates from the CES COMPAS without vertical linkages, introduction of a trade restriction increases demand for upstream goods and decreases supply of downstream goods, increasing prices of both upstream and downstream goods, while increasing shipments of upstream goods and decreasing shipments of downstream goods. In estimating the impact of the safeguard measures imposed on the flat rolled steel market, accounting for the vertical linkages is most important when estimating the impact on domestically produced slab since all downstream products produced from slab were subject to the safeguard tariffs.