With the availability of numerical modelling techniques, engineers and researchers can simulate and assess structures without the costly and laborious constraints of experimental studies. The finite element method (FEM) is a well-known and widely used modelling technique to simulate structures. In contrast, the applied element method (AEM) is a more recent technique, but is very promising in simulating extreme loading events on structures, such as earthquakes. The objective of this study is to compare both modelling approaches and the validation results of each technique by modelling two fully grouted reinforced masonry shear walls (RMSWs). SeismoStruct and Extreme Loading for Structures (ELS) are the selected software to apply the FEM and AEM, respectively. The results of each model were plotted against experimental results from the literature. Each modelling technique was able to capture the lateral cyclic performance of the fully grouted RMSWs. However, the SeismoStruct model required a significantly lower runtime compared to that of the ELS models. It was found that for fully grouted RMSWs, the FEM in SeismoStruct is the preferable modelling technique. However, this conclusion does not apply to other types of masonry walls such as partially grouted RMSWs, where SeismoStruct falls short in providing modelling tools to simulate them. Contrarily, ELS provides more flexibility for modelling in terms of element and material models. Furthermore, due to the idea of continuum mechanics in the FEM, the AEM is preferable when simulating a collapse. Modelling the separation of elements is more challenging in the FEM, whereas, in the AEM, elements are easily separated and can collide with the ground.