The tack of polymer melts on rigid substrates under conditions of short contact times and low pressures is examined. The substrate is modeled as a random rough surface with a distribution of asperities heights. The true contact area between the adhesive and the substrate is calculated for a given total load and elastic modulus of the substrate. The dependence of tack on contact time is accounted for by introducing the relaxation of the adhesive through a time-dependent elastic modulus. For relatively high pressures the tack is predicted to scale with 1/E so that for short contact times, t(c), the tack is predicted to scale with (t(c)/tau(e))(1/2), where tau(e) is the entanglement time. For lower pressures this simple scaling law is no longer valid and we predict a complex variation of tack with contact time and molecular parameters.