An evidence-theory-based interval perturbation method (ETIPM) and an evidence-theory-based subinterval perturbation method (ETSPM) are presented for the kinematic uncertainty analysis of a dual cranes system (DCS) with epistemic uncertainty. A multiple evidence variable (MEV) model that consists of evidence variables with focal elements (FEs) and basic probability assignments (BPAs) is constructed. Based on the evidence theory, an evidence-based kinematic equilibrium equation with the MEV model is equivalently transformed to several interval equations. In the ETIPM, the bounds of the luffing angular vector (LAV) with respect to every joint FE are calculated by integrating the first-order Taylor series expansion and interval algorithm. The bounds of the expectation and variance of the LAV and corresponding BPAs are calculated by using the evidence-based uncertainty quantification method. In the ETSPM, the subinterval perturbation method is introduced to decompose original FE into several small subintervals. By comparing results yielded by the ETIPM and ETSPM with those by the evidence theory-based Monte Carlo method, numerical examples show that the accuracy and computational time of the ETSPM are higher than those of the ETIPM, and the accuracy of the ETIPM and ETSPM can be significantly improved with the increase of the number of FEs and subintervals.