With the increasing popularity of multicomputers, efficient way of communication within its processors has become a popular area of research. Multicomputers refer to a computer system that has multiple processors, they have high computational power and they can perform multiple tasks concurrently. Mesh and Torus are some of the commonly used network topologies in building multicomputer systems. Their performance highly depends on the underlying network communication such as multicast. Multicast is a communication method in which a message is sent from a source node to a certain number of destinations. Two major parameters used to evaluate multicast are time that a multicast process takes to deliver the message to all destinations and traffic that indicates the number of links used for this process. Research indicates that in general, it is NPcomplete to find an optimal multicasting algorithm which is efficient on both time and traffic.This thesis suggests two new algorithms to achieve multicast in mesh and torus networks.Extensive simulations of these algorithms show that in practice they perform better than existing ones.