In order to solve the easy overestimation of classic interval algorithms for uncertainty-based damage identification of structures, an identification method is developed incorporating modal interval analysis with improved analytical redundancy reduction (IARR). Firstly the equations of structural static equilibrium are replaced by a set of constraint equations. Then the proposed improved analytical redundancy reduction algorithm is used to eliminate the rotation variables in the equations and most important of all, to make the equations related to damage components stay in the same subset. After that, the equations are expanded to interval format through adopting interval variables. Modal interval analysis is executed to evaluate the satisfaction of each constraint equation, by which means damage can be located. An experimental steel beam under a static load is used to validate the proposed method. The constraint equations for each beam segment are established based on three random parameters related to the stiffness, the deflections and the load. The analysis results demonstrate that taking into account the test error and parameter uncertainties, the proposed method can effectively locate the minor damage according to the unsatisfied constraints.