Selective repeat automatic-repeat-request (ARQ) schemes with finite receiver buffer have been studied and analyzed extensively for point-to-point communications. In this paper, we propose a selective repeat ARQ scheme for point-to-multipoint communications where each receiver has a finite buffer size. A lower bound on the throughput efficiency of the proposed scheme is obtained. Computation of the lower bound and simulation of the scheme reveal that the ARQ scheme performs quite satisfactorily, particularly for channels with large round-trip delay and high data rate like the satellite channel. The proposed scheme outperforms the full-memory go-back-N scheme proposed by Gopal, et al. [13]. The scheme seems ideally suited for the case of a satellite operating in broadcast mode with many receivers.