The enormous potential of carbon nanotubes (CNTs) as primary components in electronic devices and NEMS necessitates the understanding and predicting of the effects of mechanical deformation on electron transport in CNTs. In principle, detailed atomic/electronic calculations can provide both the deformed configuration and the resulting electrical transport behavior of the CNT. However, the computational expense of these simulations limits the size of the CNTs that can be studied with this technique, and a direct analysis of CNTs of the dimension used in nanoelectronic devices seems prohibitive at the present. Here a computationally effective mixed finite element (FE)/tight-binding (TB) approach able to simulate the electromechanical behavior of CNT devices is presented. The TB code is carefully designed to realize orders-of-magnitude reduction in computational time in calculating deformation-induced changes in electrical transport properties of the nanotubes. The FE-TB computational approach is validated in a simulation of laboratory experiments on a multiwall CNT and then used to demonstrate the role of the multiwall structure in providing robustness to conductivity in the event of imposed mechanical deformations.