In this work, the trap sensitivity of single material gate (SMG) and dual material gate (DMG) nano ribbon FETs (NRFETs) are reported using TCAD Sentaurus Device simulator. The trap sensitivity is extracted for Gaussian trap distribution of both acceptor and donor type traps. We have reported the trap sensitivity for the variation in trap concentration, energy peak position, work function of metal gate, and temperature for both the NRFETs. It is realized that trap sensitivity is greater and lesser than 100% for acceptor type trap in SMG and DMG NRFETs, respectively, whereas, such sensitivity is 147% and 123% for donor type trap concentration, respectively. Temperature also shows a significant variation in trap sensitivity for both the NRFETs. The increase in work function leads to the reduction in trap sensitivity for both NRFETs in existence of acceptor and donor trap charges. The maximum sensitivity in trap are 400% and 275% for SMG and DMG NRFETs, respectively, in presence of donor trap concentration. Moreover, the trap sensitivity is very insignificant at high gate bias for donor type trap concentration with wide variation in parameters.