One of the main problems in LTE networks is the distribution of a limited number of radio resources among Human-to-Human (H2H) users as well as the increasing number of machine-type-communication (MTC) devices in machine-to-machine (M2M) communications. Different traffic types from user's equipment and MTC devices transmitted over the network suggests a dynamic resource allocation in order to provide a better quality of service (QoS). In this paper, we propose a dynamic resource allocation scheme for M2M traffic in LTE networks. The suggested method is based on fixed bandwidth intervals at which traffic from MTC devices is serviced according to the Processor Sharing (PS) discipline. By means of a Markov model, an estimation of the behaviour of LTE for H2H and M2M traffics characteristics is shown. We propose an analytical solution to calculate the model performance measures, such as blocking probabilities for H2H users. © 2013 Springer-Verlag.