Although capacity constraints in traffic assignment can represent many realistic features, these constraints are largely ignored in practice because of mathematical complexities in applying the methods proposed in the literature. In this study such complexities are relaxed by the adoption of an intuitive interpretation for the Lagrange values of the capacity constraints, that is, the amount of penalty added to the travel time of the oversaturated links to discharge the excessive flow to the extent to which they become saturated. This penalty term bears some similarity to the marginal cost of the system optimal. Hence the capacitated traffic assignment problem (TAP) becomes a normal uncapacitated TAP in which the aforementioned additional penalty is updated iteratively. The proposed provision is flexible to accommodate TAP’s solution algorithms such as Frank–Wolfe. The main motivation of this study is to address the needs of the industry; hence, the proposed method is coded in a leading commercial transport planning software product, and a large-scale network of Winnipeg, Manitoba, Canada, is used for numerical evaluations. Furthermore the benchmark network of Hearn is also used for comparative evaluations with respect to other methods. Results suggest that in regard to the reliability of the outcomes and computational efficacy, the proposed algorithm is as good as other methods. Unlike other methods, there is no additional parameter to be calibrated, and the convergence behavior of the algorithm is promising.