Stretchable and flexible electronics has attracted broad attention over the last years. Nanocomposites based on elastomers and carbon nanotubes are a promising material for soft electronic applications. Despite the fact that single-walled carbon nanotube (SWCNT) based nanocomposites often demonstrate superior properties, the vast majority of the studies were devoted to those based on multiwalled carbon nanotubes (MWCNTs) mainly because of their higher availability and easier processing procedures. Moreover, high weight concentrations of MWCNTs are often required for high performance of the nanocomposites in electronic applications. Inspired by the recent drop in the SWCNT price, we have focused on fabrication of elastic nanocomposites with very low concentrations of SWCNTs to reduce the cost of nanocomposites further. In this work, we use a fast method of coagulation (antisolvent) precipitation to fabricate elastic composites based on thermoplastic polyurethane (TPU) and SWCNTs with a homogeneous distribution of SWCNTs in bulk TPU. Applicability of the approach is confirmed by extra low percolation threshold of 0.006 wt % and, as a consequence, by the state-of-the-art performance of fabricated elastic nanocomposites at very low SWCNT concentrations for strain sensing (gauge factor of 82 at 0.05 wt %) and EMI shielding (efficiency of 30 dB mm^–1 at 0.01 wt %).