Numerical simulations have been carried out of initially weak (shock Mach number Ms≊1.1–2.1) cylindrical shock waves propagating radially inward, simulating the experiments of Takayamaet al. (1987). Although the code employs a finite‐element technique with an unstructured (triangular) grid and neither the system geometry nor the initial conditions have any rectangular symmetry, contours of the numerical solutions (particularly the vorticity) exhibit a pronounced enhancement of them=4 component. Solution of the linearized form of the equations of geometrical shock dynamics (Whitham, 1974) reveals no preference form=4. Possible explanations for the phenomenon are suggested.