One challenging question E-business executives face is whether to construct the direct Internet channel in addition to the traditional retail channel. In this paper, we develop a model for strategic dual channel investment under uncertainty and strategic customer behaviors. Based on this model, we provide analytical solutions for thresholds that dual channel makes less profit than a single channel. Moreover, we studied the role of a cost structure for the Internet channel based on this threshold. Companies are likely to have wider inefficiency region as the cost for the Internet channel increases. We provide numerical examples to analyze the effects of price volatility, uncertainty, on the inefficiency of dual channel and the effects of an asymmetric cost structure.