Starting from the cobweb theorem, a model of demand, supply, multilateral trade, and prices was formulated for the softwood lumber and newsprint markets in Canada, the United States (US), and the rest of the world. Parameters were estimated with panel data from multiple years and countries. The model was used to project the effects of US tariffs on softwood lumber and newsprint imports from Canada. To assess the uncertainty of the projections, multiple replications were performed by repeated sampling from the parameters’ statistical distributions. The results suggested that the initial shock of the tariffs dampened out and took 3 to 4 years to stabilize. In the long run, other things being equal, a 20.83% US tariff on softwood lumber imports from Canada decreased US imports from Canada by 4.7% to 8.0% and raised the US price by 0.3% to 2.3% and the US production by 0.9% to 1.7%, with 95% probability, while it lowered the Canadian price by 0.7% to 3.0% and Canadian production by 1.1% to 2.4%. A 28.69% US tariff on newsprint imports from Canada decreased US imports from Canada by 3.2% to 7.0% and raised the US price by 1.4% to 3.3% and the US production by 2.9 to 6.3%, while it lowered the Canadian price by 0.8% to 1.9% and the Canadian production by 1.6% to 3.5%.