This theoretical study focuses on junctions between the carbon nanotubes (CNTs) and contacting metallic elements of a nanocircuit. Numerical simulations on the conductance and resistance of these contacts have been performed using the multiple scattering theory and the effective media cluster approach. Two models for CNT-metal contacts have been considered in this paper: a) first principles “liquid metal” model and b) semi-empirical model of “effective bonds” based on Landauer notions on ballistic conductivity. Within the latter, which is a more adequate description of chirality effects, we have simulated both single-wall (SW) and multi-wall (MW) CNTs with different morphology. Results of calculations on resistance for different CNT-Me contacts look quantitatively realistic (from several to hundreds kOhm, depending on chirality, diameter and thickness of MW CNT). The inter-wall transparency coefficient for MW CNT has been also simulated, as an indicator of possible ‘radial current’ losses.