We investigate freely expanding viscoelastic sheets. The sheets are produced by the impact of drops on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation as a result of the cold Leidenfrost effect. The time evolution of the sheet is simultaneously recorded from top and side views using high-speed cameras. The investigated viscoelastic fluids are Maxwell fluids, which are characterized by low elastic moduli, and relaxation times that vary over almost two orders of magnitude, thus giving access to a large spectrum of viscoelastic and elastocapillary effects. For the purposes of comparison, Newtonian fluids, with viscosity varying over three orders of magnitude, are also investigated. In this study, d(max), the maximal expansion of the sheets, and t(max) the time to reach this maximal expansion from the time at impact, are measured as a function of the impact velocity. By using a generalized damped harmonic oscillator model, we rationalize the role of capillarity, bulk elasticity and viscous dissipation in the expansion dynamics of all investigated samples. In the model, the spring constant is a combination of the surface tension and the bulk dynamic elastic modulus. The time-varying damping coefficient is associated to biaxial extensional viscous dissipation and is proportional to the dynamic loss modulus. For all samples, we find that the model reproduces accurately the experimental data for d(max) and t(max).