The prediction of the change in the conductivity of carbon nanotubes (CNTs) and graphene nanoribbons (GNRs) under strain is very important to assure the reliability of the performance of CNT-based devices, such as transistors, sensors, actuators, etc. In this study, the change of the electronic state of CNTs and GNRs caused by their deformation was analyzed. We found that the change of the electronic sate of CNTs was mainly dominated by two factors; (a) distortion of a six-membered ring due to the change in the C-C bond length and (b) increase in the local curvature of the tube. The increase of the curvature caused the orbital hybridization. The electronic state of GNRs also changed drastically when the hybridization was occurred by the curvature deformation.