Cosmic filaments constitute one of the most prominent components of the large-scale structure of the Universe, forming coherent, elongated bridges between clusters and superclusters of galaxies. In the standard cosmological framework, these structures are interpreted as dark-matter-dominated density enhancements produced by the gravitational amplification of primordial fluctuations. In this work, we explore an alternative description based on Vacuum Localized Structures (VLS): self-gravitating solutions of the Einstein field equations characterized by a non-standard vacuum equation of state.We derive and analyze a new class of exact, cylindrically symmetric VLS solutions of the Einstein equations, appropriate to modelling extended filamentary systems. These solutions are supported by an effective stress—energy tensor with radial pressure p_r=-ρ/3, generalising the equation of state previously identified in spherical VLS configurations. We characterise the resulting space-time, study its gravitational field, and show that it naturally gives rise to coherent, non-singular, extended structures with finite mass per unit length.The present cylindrical solutions extend earlier work on spherical VLS, where galactic-scale configurations were shown to reproduce key features of observed rotation curves without invoking particle dark matter. Taken together, the spherical and cylindrical solutions provide a unified relativistic framework in which both galactic halos and cosmic filaments emerge as manifestations of vacuum-organized gravitational structures.We discuss the physical properties of cylindrical VLS, their potential stability, and their relevance to observed filament phenomenology, including coherence length, mass distribution, and large-scale dynamical effects. These results suggest that vacuum localized structures may offer a viable alternative foundation for the gravitational scaffolding of the cosmic web.