A filament model has been applied to 3D simulations of an Inductively Coupled Plasma (ICP). The filament model allows independent meshing of one-dimensional (long and slender) objects embedded into multi-dimensional space. It greatly facilitates the problem set up and substantially reduces the number of computational cells. We have demonstrated the usage of filament model for the set-up of multi-spiral coil and gas injectors in a plasma reactor and illustrated the sensitivity of spatial plasma distribution on coil design and gas flow patterns for a low pressure ICP reactor in argon gas.