The linear stability of turbulent shear flow over a film-covered sea surface is studied theoretically. A compound matrix method (Wheless & Csanady 1993), is used to solve the eigenvalue problem numerically. The numerical method has been adjusted to a coupled air–sea system. In the stability problem the vertical component of the turbulent Reynolds stress has been taken into account. As pointed out by Wheless & Csanady, the second derivative of the traditional log–linear wind profile has a rather extreme behaviour near the matching point of the linear and logarithmic part. To improve the model, a new profile is calculated based on an eddy viscosity distribution for channel flow (Quarmby & Anand 1969), which has continuous derivatives all the way down to the surface. Calculations of the wave growth rates corresponds well with earlier theoretical results as well as laboratory measurements. The energy flux from the air to the sea caused by the pressure work at the surface has been calculated. An intriguing result obtained here is that this flux seems to be strongly dependent on the elastic property of the surface film. The flux attains a maximum for finite values of the film elasticity parameter.