The previous study of virtual path design for one traffic class with ATM DCS only should be generalized to that for the multiple traffic class cases of being given neither virtual path candidate set nor end nodes o each virtual path. In this paper, a design model of virtual paths for the general case with multiple traffic classes is suggested. The model is represented as an optimization rpoblem with a special structure. It is solved by SQA algorithm, which is developed by authors in [3, 4]. The model and the algorithm are applied to a numerical example, and results are shown.