In this paper, we present a novel control-theoretic explicit rate (ER) allocation algorithm for the MAX-MIN flow control of elastic traffic services with minimum rate guarantee in the setting of the ATM available bit rate (ABR) service. The proposed ER algorithm is simple in that the number of operations required to compute it at a switch is minimized, scalable in that per-virtual-circuit (VC) operations including per-VC queueing, per-VC accounting, and per-VC state management are virtually removed, and stable in that by employing it, the user transmission rates and the network queues are asymptotically stabilized at a unique equilibrium point at which MAX-MIN fairness with minimum rate guarantee and target queue lengths are achieved, respectively. To improve the speed of convergence, we normalize the controller gains of the algorithm by the estimate of the number of locally bottle-necked VCs, The estimation scheme is also computationally simple and scalable since it does not require per-VC accounting either. We analyze the theoretical performance of the proposed algorithm and verify its agreement with the practical performance through simulations in the case of multiple bottleneck nodes. We believe that the proposed algorithm will serve as an encouraging solution to the MAX-MIN flow control of elastic traffic services, the deployment of which has been debated long due to their lack of theoretical foundation and implementation complexity.