Although EU and Turkey are integrated by Customs Union since 1996, there are still quota limits to Turkish road transport in some European countries. These quotas cause concerns related to increased transportation costs, which will in turn increase the costs of export goods and create important barriers to international trade. In this study, the effects of quotas on Turkish foreign trade with EU countries are investigated using an integrated multicommodity flow model and a gravity model. The classical multi-commodity network flow model is innovatively used to predict the costs of transportation with and without the transit and bilateral quotas applied by the European countries. As a result, the extra costs originating from the quotas are forecasted. These extra costs are used in a gravity model to analyze their effect on international trade. The gravity model is estimated with panel data related to 17 selected European countries between 2009 and 2015. The results indicate that the costs originating from the quotas have significant effects on Turkish total exports, and exports of food and beverages and the machinery and equipment sectors. The size of the losses in the total export and the selected sectors are also calculated by using a scenario analysis.