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One-dimensional carbon nanotubes (CNTs) are promising for future nanoelectronics and optoelectronics, and an understanding of electrical contacts is essential for developing these technologies. Although significant efforts have been made in this direction, the quantitative behavior of electrical contacts remains poorly understood. Here, we investigate the effect of metal deformations on the gate voltage dependence of the conductance of metallic armchair and zigzag CNT field effect transistors (FETs). We employ density functional theory calculations of deformed CNTs under metal contacts to demonstrate that the current-voltage characteristics of the FET devices are qualitatively different from those expected for metallic CNT. We predict that, in the case of armchair CNT, the gate-voltage dependence of the conductance shows an ON/OFF ratio of about a factor of two, nearly independent of temperature. We attribute the simulated behavior to modification of the band structure under the metals caused by deformation. Our comprehensive model predicts a distinct feature of conductance modulation in armchair CNTFETs induced by the deformation of the CNT band structure. At the same time, the deformation in zigzag metallic CNTs leads to a band crossing but not to a bandgap opening.