To analyze network QoS (Quality of Service) performance and better utilize network resources, this paper develops an analytical model of QoS class mapping for hybrid QoS domains based on network calculus theory. Based on this model, an elastic QoS Mapping scheme with Flow Aggregate (EQM-FA) is proposed to support end-to-end QoS of multimedia services over heterogeneous wireless networks. In EQM-FA, the QoS requirements of service flows are indicated by a unique flow aggregate identifier which can be described by the information describing QoS on a service flow map which is a multidimensional space of relevant QoS parameters. With flow aggregate identifier and mapping executors sitting at the border of different QoS domains, EQM-FA allows smooth QoS class mapping between different networks with different granularity of QoS class. Both numerical analysis and simulation studies are given to demonstrate the efficacy of the proposed method.