Confluences are basic building blocks in river networks at all scales. When two rivers merge at a confluence, rapid changes in fluid velocity and turbulence intensity cause changes in the bed geometry. Usually, a deep scour hole and a depositional point bar are present at the confluence. One important phenomenon that has been overlooked in previous studies is the progressive penetration of the scour hole into the tributary channel. This progressive penetration may jeopardize the structural safety of the lateral channel in the proximity of the main channel. In this study, dimensional analysis techniques are used to develop a general equation for the prediction of maximum scour hole penetration (Psc) into the tributary. Eventhough, the penetration of the scour hole into the lateral channel is a time-dependent process, in developing the formula the maximum value after the equilibrium condition has been achieved is used. A series of 73 experimental tests with different confluence angle (θ), lateral to downstream channel discharge ratio (Qr), lateral to main channel width ratio (Br) and downstream densimetric Froude number (Fg) in an asymmetrical confluence has been conducted to test the proposed formulation. The results show that Psc increases with Qr, θ and Fg and decreases with Br. The degree of penetration defines two types of scour holes: In the first type the scour hole penetration only reaches the toe of the lateral channel wall closer to the downstream junction corner whereas in the second type the scour hole reaches both lateral channel walls. The second type is associated with higher values of Qr, θ and Fg and lower values of Br. Statistical analysis showed that the mean error of the developed formula is of the order of 24%.