Relevant CNT-metal contacts belong to so-called extended type. Current flows from electrodes into CNT in a distributed manner, and contact resistance depends on the contact length. In such circumstances the standard ab-initio based transport techniques to calculate electron transport should be modified. We have developed a special method which allows calculation of transport in the systems with metal-CNT contacts at ab-initio level. It takes into account both internal and external parts of the CNT-metal contact and requires simulation of the one principal and two auxiliary atomistic systems. Results of ab-initio calculations are then subjected to special treatment and being used in Green function formalism afterwards. This method was applied to Al-CNT and Pd-CNT extended contacts. Results agree perfectly with existing experimental data being indeed obtained at a purely ab-initio level.