Abstract—Mission Critical communication is promising communication and services technology for emergencies and catastrophes. The progress in technology and development of mission-critical Device-to-Device (D2D) communication is reviewed in this study. Two novel models for dedicated and reuse D2D have been proposed with Rayleigh fading and path loss in mission critical application. In this study the mathematical expressions for the Signal to Interference Plus Noise Ratio (SINR) and system rate computation for mission critical communication have been derived. The mission critical application models have been simulated and results have been analyzed for SINR in single cell scenario when two nearby devices communicate directly, and for larger distances communication using base station. In dedicated mode, the SNR outperforms at short ranges. However, in reuse mode, communication through base station maintains high SINR. The system performance with the models in this paper shows potential advantages and can facilitate trade off selection of technology and thus is important in design of applications and system for mission critical applications.