One of the main problems in LTE networks is distribution of a limited number of radio resources among Human-to-Human (H2H) users and increasing number of machine-type-communication (MTC) devices in machine-to-machine (M2M) communications. The radio resources allocation scheme of M2M traffic service in LTE networks discussed in the paper is adopted by 3GPP and implements Random Access Channel (RACH) mechanism for transmitting data units from a plurality of MTC devices. This mechanism determines the sequence of signaling messages transmitted between a MTC device and a ENodeB (eNB) without reserving radio resources. The mathematical model for calculation of the mean time from the instant of MTC device activation to the instant of data transition beginning via eNB is built. The Monte Carlo method for simulation the behavior of the system is used. © 2014 Springer International Publishing.