This paper reports the results of studies on the rheological behavior of nanocomposites of high density polyethylene (HDPE) with pristine multiwall carbon nanotubes (CNT) as well as phenol and 1‐octadecanol (C18) functionalized CNT at 1, 2, 3, 4, 5, and 7 wt% loading. The viscosity reduction at 1 wt% CNT follows the order, pristine CNT < phenol functionalized CNT < C18 functionalized CNT. As the filler loading increases from 1 to 2, 3, and 4 wt%, neat HDPE and filled HDPE systems show similar moduli and viscosity, particularly in the low frequency region. As the filler loading increases further to 5 and 7 wt%, the viscosity and moduli become greater than the neat HDPE. The storage modulus, tanδ, and the Cole‐Cole plots show that CNT network formation occurs at higher CNT loading. The critical CNT loading or the rheological percolation threshold, where network formation occurs is found to be strongly dependant on the functionalization of CNT. For pristine CNT, the rheological percolation threshold is around 4 wt%, but for functionalized CNT it is around 7 wt%. The surface morphologies of CNT and functionalized CNT at 1 wt% loading showed good dispersion while at 7 wt% loading, dispersion was also achieved, but there are few regions with agglomeration of CNT.