The inherent low thermal conductivity and inferior mechanical properties of polymer based shape stabilised phase change materials (SSPCMs) restrict their wide applications in building sections. Multi-walled carbon nanotubes (MWCNTs) with excellent thermal and mechanical properties were incorporated into SSPCMs based on blends of a low molecular weight HDPE (lv-HDPE) and paraffin waxes by extrusion. Their suitability for latent heat thermal energy storage was evaluated. The MWCNTs were uniformly distributed within the SSPCM matrix and were wetted by the SSPCM. The SSPCMs with MWCNTs had latent heats up to 53 J g−1 with 0.5 wt% MWCNTs. Both the Young's moduli and yield stress of lv-HDPE50H-PW50 with MWCNTs composites were lower than that of unfilled lv-HDPE50H-PW50 at low MWCNT loading (≤1 wt%). They then went up with an increase in MWCNT loading (from 1 wt% to 3 wt%). This is due to the formation of an inter-connected network of MWCNTs. Similar results were obtained for both flexural moduli and stress. However, there is no significant difference of the compression moduli between unfilled lv-HDPE50H-PW50 blend and those MWCNT blends. The thermal conductivity increased with increasing MWCNTs content and the greatest enhancement was 29 % for SSPCM with 3 wt% MWCNTs. It will therefore contribute to the decarbonisation of buildings.