In this article, a new algorithm for the computation of workspace boundaries of continuum parallel robots (CPRs) is proposed. State-of-the-art techniques are mainly based on time-consuming joint space discretization approaches or task-space discretization algorithms, and only a few approaches are dedicated to the computation of workspace boundaries. The proposed approach for the computation of the workspace boundaries is based on (i) a free-space exploration strategy and (ii) a boundary reconstruction algorithm. The former is exploited to identify an initial workspace boundary location (exterior, interior boundaries, and holes), while the latter is used to reconstruct the complete boundary surface. Moreover, the algorithm is designed to be employed with CPR modeling strategies based on general discretization assumptions, in order to increase its applicability for various scopes. Our method is compared with two state-of-the-art algorithms in four cases studies, to validate the results and to establish its merits and limitations.