Bipedal robots capable of various dynamic motions such as walking, running, and jumping have been developed in recent years. In particular, these dynamic motions require the use of high power in a short time when the robot kicks off the ground. Furthermore, it is necessary to decrease the impact force that a robot is subjected to when landing during these motions. Unfortunately, rigid actuators tend to become heavier as their output increases. Therefore, we focus on the method for obtaining a high output using elastic energy. However, the use of the elastic element only leads to robot vibration. Therefore, to control the dynamic motion, we adopted the viscosity element to the robot joint. In this study, we focused on a straight-fiber-type artificial muscle for the elastic element and a magnetorheological brake for the viscosity and friction elements, respectively. A previously designed monopedal robot was able to jump 82.5 mm using a sliding rail and counter weights; however, the robot shook upon landing because of the presence of the elastic element in its artificial muscles. In this paper, we first proposed a dynamic model of the previously developed monopedal robot. We then performed vertical jumping simulations of the robot to confirm the model's utility.