Alfvén wave propagation is studied in an incompressible fluid stratified by an inhomogeneous fluid density or magnetic field strength. It is shown that any disturbance splits up into two components—an ordinary Alfvén mode and a modified Alfvén mode. The first of these propagates one‐dimensionally along flux tubes at the local Alfvén speed while the second propagates three‐dimensionally and carries a disturbance in the total (fluid plus magnetic) pressure.