Generalizing the results obtained by Stix (1970) and by Whitehead (1971), we present the homogeneous boundary conditions that are imposed by a fluid of stable but otherwise arbitrary stratification. These penetrative conditions are strictly valid only in the limit of steady linearized flow, but under some conditions they can also be applied to nonlinear problems. An example of linear penetrative convection is treated in order to illustrate the use of these boundary conditions.