The separation of two plates bridged by a thin layer of a viscoelastic liquid (polymer solution) leads to complex instabilities. The larger fingering structure corresponds to a Saffman-Taylor instability: a fluid of low viscosity (air) penetrate into a viscous liquid which generates viscous fingering. Elastic stresses in the solution are also induced when the polymeric molecules get stretched enough. They are responsible for the secondary structure which develops at larger strains.