In the Mach reflection of weak shock waves, there has been a wide difference between theory and experiment for the shock wave angles at the triple point. Using the electric tank analogy in the hodograph to obtain the shock patterns it is found that the shock waves are so strongly curved near the intersection that the triple point angles cannot be observed in the laboratory. However, it is shown that the visible shock patterns are apparently inconsistent with the hodograph boundaries specified by the existing triple point theory. The effect of shock wave thickness on the boundary conditions at the triple point is then examined. It is shown that at the intersection there must be a non‐Rankine‐Hugoniot shock wave zone separating the three R‐H shock waves. It follows that for weak shock waves where the shock curvatures → ∞ at the triple point, the simple boundary conditions of equal pressure and direction are invalid for a real fluid. A semiquantitative description is then given of a real fluid model which is consistent with the experimental data and with the Navier‐Stokes equations. The examination of this model reveals the formidable difficulties in the way of obtaining a detailed mathematical description of a triple shock wave intersection in a real fluid. The question of the solution for the limiting case as &mgr; → 0 is also discussed.