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Snap-off of bubbles and drops in constricted capillaries occurs in many different situations, from bio-fluid to multiphase flowin porous media. The breakup process has been extensively analyzed both by theory and experiments, but most work has been limited to pure interfaces, at which the surface stress is isotropic and fully defined by the interfacial tension and interface curvature. Complex interfaces may present viscous and elastic behavior leading to a complex stress state that may change the dynamics of the interface deformation and breakup. We extend the available asymptotic model based on lubrication approximation to include elastic interfacial stress. Drop breakup time is determined as a function of the capillary geometry and liquid properties, including the interfacial elastic modulus. Results show that the interfacial elasticity has a stabilizing effect by slowing down the growth of the liquid collar, leading to a larger break-up time. This stabilizing effect has been observed experimentally in different, but related flows [Alvarado et al., "Interfacial visco-elasticity of crude oil-brine: An alternative EOR mechanism in smart waterflooding," in SPE-169127 Improved Oil Recovery Symposium (Society of Petroleum Engineers, 2014)]. [ABSTRACT FROM AUTHOR]