Fluid Bridges are structures generated by the influence of the capillary forces in a two fluid interface (air-fluid). Nowadays there are many works describing its behavior due to its importance in many fields (from biomedical engineering to non-gravity applications). This work pretends to not only describe, simulate and analyze these structures behavior but also adapt the one-dimensional model (where a Newtonian fluid is trapped between two solid plates and one of them distances from the other with a constant velocity) with an elastic Interface. Because of that, the surface tension stops being isotropic and new equations need to be developed and solved. Appropriate numeric techniques are used to do that so the results match the actual behavior of the amended bridge Results show that high viscosity fluids bridges tends to be more stable and need more time for the break-up of the structure. Not only the viscosity but also the stretching velocity, initial volume and elasticity factor play major roles in the simulations. Finally, it is show that the break-up time behave exponentially based on the elasticity factor.