Machine-to-machine (M2M) communications and applications are expected to be a significant part of the next generation 5G networks. While there have been a large amount of research studies with respect to radio resource management, load balancing, and devices grouping for M2M communications, few of them has addressed the issue of admission control. In this paper, we propose a new admission control model for M2M communications, which classifies all M2M requests into delay-sensitive and delay-tolerant first, and then aggregates all delay-tolerant requests, aiming to reduce the number of requests from devices to base stations. An admission control algorithm based on this model is devised to prevent congestion and to improve the quality of services, and a network calculus based performance-analyzing technique is developed for this model. Both theoretical analyses and simulation results show that the proposed model is feasible and valid.