Multicast is message propagation from a source node to a number of destination nodes. Multicast could become the bottleneck for the performance of processes and systems. The main parameters for evaluating a multicast are time and traffic. Optimizing multicast time and traffic is proven to be NP-hard. In this paper, we propose improvements on two tree based multicast algorithms, PAIR and DIAG, in 2D mesh and torus networks. We prove that MDIAG generates optimal or optimal plus one multicast time in 2D meshes. MDIAG has lower complexity than DIAG, but might generate more traffic. MPAIR generates the least traffic, has the same complexity as PAIR and better complexity than DIAG, but might generate more time. The average time generated by both algorithms in a 2D torus is almost half the average time generated in a 2D mesh for the same algorithm. The average traffic generated by both algorithms in a 2D torus is less than the average traffic generated in a 2D mesh in most cases for the same algorithm. Extensive simulations of the algorithms show that they perform better than existing ones.