AbstractThe character of equilibrium of an incompressible visco‐elastic fluid of variable density stratified in the vertical direction has been investigated. It is demonstrated that the solution is characterized by a variational principle. Use has been made of this principle to obtain approximate solution for an Oldroyd fluid of exponentially varying density confined between two horizontal boundaries. It is shown that the rate at which the system departs from equilibrium increases with the stress relaxation time and decreases as the strain retardation time increases. For a configuration in which gravity effects are ignored, it is found that the waves can be excited for some disturbances for which no oscillatory motion is possible in a newtonian fluid. The effects of rotation are also considered. Finally the usefulness of variational principle is checked by comparing some exact results with approximate one