Damage detection of civil and mechanical structures based on measured modal parameters using model updating schemes has received increasing attention in recent years. In this study, for uncertainty‐oriented damage identification, a non‐probabilistic structural damage identification (NSDI) technique based on an optimization algorithm and interval mathematics is proposed. In order to take into account the uncertainty quantification, the elastic modulus is described as unknown‐but‐bounded interval values and the proposed new scheme determines the upper and lower bounds of the damage index. In this method, the interval bounds can provide supports for structural health diagnosis under uncertain conditions by considering the uncertainties in the variables of optimization algorithm. The model updating scheme is subsequently used to predict the intervalbound of the Elemental Stiffness Parameter (ESP). The slime mold algorithm (SMA) is used as the main algorithm for model updating. In addition, in this study, an enhanced variant of SMA (ESMA) is developed, which removes unchanged variables after a defined number of iterations. The method is implemented on three well‐known numerical examples in the domain of structural health monitoring under single damage and multi‐damage scenarios with different degrees of uncertainty. The results show that the proposed NSDI methodology has reduced computation time, by at least 30%, in comparison with the probabilistic methods. Furthermore, ESMA has the capability to detect damaged elements with higher certainty and lower computation cost in comparison with the original SMA.