Recently, wormhole routers with multi-destination capability have been proposed to support fast multicast in a multi-computer network. In this paper, we develop a new multicasting model for such networks based on the concept of Euler path/circuit in graph theory. The model can support multiple concurrent multicasts freely from deadlock and can be applied to any network which is Eulerian or is Eulerian after some links being removed. No virtual channels are needed. In particular, we demonstrate the potential of this model by showing its fault-tolerant capability in supporting multicasting in the currently popular torus/mesh topology of any dimension with regular fault patterns (such as single node, block, L-shape, +-shape, U-shape, and H-shape) and even irregular fault patterns. The result has improved over existing fault-tolerant routing algorithms for meshes/tori in at least one of the following aspects: the number of faults tolerable, the shape of fault patterns, the number of deactivated healthy nodes, the requirement of support of virtual channels, and the range of network topology acceptable.