Simulating dense interactions of multiple characters in real-time is an important research topic that has many applications such as 3D games and virtual reality systems. There are many issues that have to be overcome to achieve that goal. Most importantly, a framework to generate reactive motions of virtual humans when they are hit, pushed and pulled must be proposed. Although some researchers have worked on reactive motion synthesis of virtual human by using dynamics, they do not consider motions with changing contact state such as walking or running, in which the supporting pattern changes periodically. Only the balance of the body of the virtual character is considered. In this thesis, we propose a new method to simulate reactive motions during arbitrary bipedal activities, such as standing, walking or running. It is based on momentum-based inverse kinematics and motion blending. When generating the animation, the user first imports the primary motion to which the perturbation is applied. According to the condition of the impact, the system selects an appropriate reactive motion from the database of pre-captured stepping and reactive motions. It then blends the selected motion into the primary motion using momentum-based IK. Since the reactive motions can be edited in real-time, the criterion for motion search can be much relaxed than previous methods, and therefore, the computational cost for motion search can be reduced. With our method, it is possible to generate reactive motions by applying external perturbations to the characters at arbitrary moment while they are performing some actions. We have carried out some experiments to evaluate the performance of the proposed method. According to the experimental results, the computation of IK becomes the bottleneck when editing the motion of multiple characters simultaneously in a single scene using this method. Therefore, when there are many characters and constraints, an efficient IK solver is needed for real-time reactive motion synthesis. In order to enhance the performance of the proposed reactive human motion synthesis method for multiple characters, we further propose a Linear Programming based IK solver (LPIK) for interactive control of arbitrary articulated structures. There are several advantages of using LPIK. First, inequality constraints can be handled, and therefore the ranges of the DOFs and collisions of the body with other obstacles can be handled easily. Second, the performance of LPIK is comparable or sometimes better than the IK method based on Lagrange multipliers, which is known as the best IK solver today. The computation time by LPIK increases only linearly proportional to the number of constraints or DOFs. Hence, LPIK is a suitable approach for controlling articulated systems with large DOFs and constraints for real-time applications. By combining the two proposed methods, it is possible to simulate dense interactions of multiple characters in real-time. This helps simulate scenes such as American football, basketball or chaotic crowds.