This work considers the mechanics of tack in viscoelastic materials. We study a particular tack test in which a flat, rigid probe is brought into contact with the rough surface of a viscoelastic material. The rough surface is modeled as consisting of many spherical asperities of varying heights but all having the same radius. Because of the asperities, the apparent contact area can be much greater than the actual contact area, which is regarded as the key parameter that controls tack. We show how this actual contact area evolves with time under different loading conditions. Our formulation is different from previous theories in that it explicitly accounts for the fact that asperities of different heights are subjected to different loading histories. Explicit solutions are given for the cases of a constant load test, a load relaxation test, and a constant displacement rate test.