The present work deals with the study of drop formation of polymeric fluids with the objective of providing a correlation between fluid printability and its rheological properties. An innovative approach combining together many experiments and numerical simulations of free surface flows is proposed. Viscoelasticity of fluids is probed using experimental methods that give access to the frequency, strain and strain rate domains of the drop on demand jetting process. High frequency viscoelastic measurements are performed using a Piezo Axial Vibrator (PAV) that enables linear viscoelastic measurements (LVE) to be obtained in the range 1Hz - 10 kHz. Non linear viscoelastic (NLVE) measurements are performed using the “Cambridge Trimaster”, a filament stretching apparatus that enables nonlinear stretching and filament break up to be observed at strains similar to that found in DOD. A series of low viscosity fluids possessing similar shear properties but differing by their elastic properties are used in this study. Polymer addition is found to develop fluid viscoelasticity and, in particular, an increase in the relaxation times at large strain extensional flows. Besides these different experiments, a numerical investigation of the stretching process is also performed with the development of a one-dimensional model coupled with the Arbitrary Lagrangian Eulerian (ALE) formulation. After preliminary comparison for the Newtonian case, the polymers solutions are modeled using FENE-CR constitutive equations. The predicted diameter of the middle of the thinning filament is compared against measurements obtained with the “Cambridge Trimaster” and a good agreement is found. The dynamics of drop formation and pinch-off of the above mentioned fluids are further investigated using pendant drop formation from a nozzle under the influence of gravity. The same one-dimensional model, with parameters obtained from filament thinning, is used to model the faucet phenomenon. Transient lengths and diameters of filaments are compared with experimental measurements and demonstrate the close resemblance between the two processes although the filament stretching and thinning is more controllable and allows to have access to higher Hencky strains as compared to the pendant drop technique. The ability to model the fluids in two very different flow situations allow to predict their behavior in a drop on demand process and to propose an optimization of the printing process through the use of appropriate dimensionless numbers.