The refraction of acoustical waves by a moving medium layer is theoretically treated and the reflection and transmission coefficients are determined. The moving‐medium‐layer velocity is uniform but with a space dependence in one direction. A partitioning of the moving medium layer into constant‐velocity sublayers is introduced and numerical results for a three‐sublayer approximation of Poiseuille flow are presented. The degenerate case of a single constant‐velocity layer is also treated theoretically and numerically. The numerical results show the reflection and transmission coefficients as functions of the peak moving‐medium‐layer normalized velocity for several angles of incidence.