This work proposes an analytic framework to estimate the capacity of the link in an M2M gateway that multiplexes a massive number of machine type communication devices. First, we specify the network architecture for M2M communications. Next, we summarize the characteristics of M2M traffic, from which we extract an area about the problem that has to be resolved in the dimensioning of the link capacity. After that we propose a new method to determine the capacity of the link in an M2M gateway. Via numerical experiment reflecting the realistic environment of M2M traffic, we illustrate the validity of the proposed model.