Poly(phenylacetylene) sheets that mimic the geometry of a wine‐rack‐like structure have been predicted to exhibit negative Poisson's ratios off‐axis. However, their potential to exhibit negative linear compressibility (NLC) has remained largely unexplored. In this work, the compressibility and other mechanical properties of wine‐rack‐like poly(phenylacetylene) networks with 1,2,4,5 tetra‐substituted phenyls as well as their equivalent with allene or cyclobutadiene centres are simulated to assess their ability to exhibit negative linear compressibility on‐axis and off‐axis. It is shown that some of these systems can indeed exhibit negative linear compressibility whilst others exhibit a near‐zero compressibility. The results are compared to the compressibility properties of other poly(phenylacetylene) networks reported in literature as well as with those predicted from the analytical model for an idealised wine‐rack structure deforming through hinging. Results suggest that these mechanical properties are arising from a wine‐rack‐like mechanism, and there is a good agreement with the theoretical model, especially for systems with longer acetylene chains whose geometry is closer to that of the idealised wine‐rack.