In this study, a newly developed unconditionally stable explicit method is employed to solve momentum equations of motion in performing pseudodynamic tests. Due to the explicitness of each time step this pseudodynamic algorithm can be explicitly implemented, and thus its implementation is simple when compared to an implicit pseudodynamic algorithm. In addition, the unconditional stability might be the most promising property of this algorithm in performing pseudodynamic tests. Furthermore, it can have the improved properties if using momentum equations of motion instead of force equations of motion for the step-by-step integration. These characteristics are thoroughly verified analytically and/or numerically. In addition, actual pseudodynamic tests are performed to confirm the superiority of this pseudodynamic algorithm.