The wrench-feasible workspace (WFW) of a parallel cable-driven mechanism is the set of poses of its mobile platform for which the cables can balance any wrench in a specifed set of wrenches, such that the tension in each cable remains within a prescribed range. The WFW is fundamental since it takes into account both the requirement of nonnegative cable tension and the requirement of a maximum admissible cable tension. This paper addresses the problem of the determination of the WFW of n-degree-of-freedom parallel mechanisms driven by more than n cables. Interval analysis based methods that allow to determine if a given n-dimensional box is fully included in the WFW are presented. Moreover, these methods are also able to approximate the WFW up to a chosen accuracy. The resulting approximation consists of a set of n-dimensional boxes such that each box of the set is fully included in the WFW.