AbstractA modification of Hiemenz's two‐dimensional outer potential stagnation‐point flow of strain rate a is obtained by adding periodic radial and azimuthal velocities of the form and , respectively, where b is a shear rate. This leads to the discovery of a new family of three‐dimensional viscous stagnation‐point flows depending on the shear‐to‐strain‐rate ratio that exist over the range with reflectional symmetry about . Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large‐γ asymptotic behaviors. Sample similarity velocity profiles are also presented. It is noted that the results presented here are in many ways similar to the results reported for non‐axisymmetric Homann stagnation‐point flow.