We present a Lagrangian description of the deformations. of flat Alexander polymer brushes. An Alexander brush is one in which all polymer chains are stretched from the base to the free surface of the brush. We analyze the linear stability of a grafted brush and a symmetric diblock lamella in a melt state. Both systems are unstable against plane-wave surface deformations of short wavelengths. Stability can be recovered with the introduction of a small but finite surface tension.