The ejection of liquids through round nozzles is a commonplace process in many industrial applications, from inkjet printing to bottling of consumer products. In this work, a Computational Fluid Dynamics model of the ejection of inelastic and elastic liquids through a round capillary tube has been developed to assess the influence of the ejection’s duration and velocity on the regimes of jet/droplet formation. Simulations have been performed at different Weissenberg and Ohnesorge numbers to further assess the impact of the fluid’s physical properties on the observed flow regimes. Several regimes have been identified: no fluid detachment, single droplet formation, and breakup into several droplets. The presence of elasticity has been observed to delay the breakup of droplets from the nozzle. More importantly, the results show that the injection time has an impact on the dynamics of droplet formation, having a crucial role on the process design of various industrial applications.