Extensive investigations have been conducted to study the lateral behavior of URM walls in quasi-static loading conditions. However, these investigations do not fully capture the complexity of the responses observed in real-world structures under dynamic loads. As efficient alternatives to experimental testing, various computational techniques suitable for dynamic analysis of URM structures under seismic actions have been developed. However, the literature review reveals inconsistencies in the approaches adopted by numerical models for incorporating damping, which is key for accurately simulating dynamic behaviors. This study investigates the capabilities of two 3D simplified micro-scale finite element numerical models for dynamic analysis of URM: the interface-based block-by-block models of Aref and Dolatshahi [1] and D’Altri et al [2]. The challenges arising from a dynamic setting, along with the limitations of using explicit- (for the former model) and implicit-based (for the latter) solvers are comprehensively discussed. Procedures for calibrating the inputs of options provided by each model for incorporating damping in the response are proposed, alongside techniques for optimizing their computational costs. The reliability of these calibrated models is verified by simulating the response of the out-of-plane shake-table tests on single- and multi-block dry-joint rocking walls, as well as two-way and one-way bending calcium silicate brick walls, as documented in the literature. It is found that relying on the classical Rayleigh damping in the blocks can effectively yield the desired outcome in both models, with results sufficiently matching the experimental behavior, thereby eliminating the need to consider damping in the response of mortar interfaces. However, the numerical damping effects resulting from scaling the time increments and the enhanced usability of the damping coefficient in the interfaces of the implicit model make it more applicable to a greater variety of structural cases. Moreover, the explicit model demonstrates significantly longer computational times than the implicit model in dynamic analyses, despite its superior performance in quasi-static simulations. It is also shown that for each selected structure, damping effects vary when different time histories are applied, as well as when the intensity of the load increases.