In this paper we present an algorithm to construct low-cost source trees for multicast with multiple QoS constraints and dynamic membership. Assuming the availability of link-state information, a join path is computed for a new joining multicast receiver. An algebraic formulation is introduced to show how to determine if the QoS requirements for a new receiver can be satisfied at an intermediate node along the join path and how to adjust the tree without breaking QoS requirements for existing members if they are not. Our scheme builds multicast tree incrementally and thus supports fully dynamic membership. It also supports heterogeneous receivers seamlessly. Moreover, our algorithm can support any number of arbitrary QoS metrics without assuming any dependencies among them, if they satisfy some normal mathematical property. If implemented in a distributed fashion, our approach doesn’t require any node to have explicit knowledge of the multicast tree topology, thus it scales well for multicast of large group. Simulation studies have been carried out to study the behavior of our algorithm and compare its performance with other schemes.