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Abstract We present a strategy for estimating the mass per unit length along supercluster-scale filaments that are oriented across the sky, based on mock redshift surveys of 264 filaments from the Millennium simulation. In our fiducial scenario, we place each simulated filament at a distance of 300 Mpc, perpendicular to the line of sight, and calculate the redshift dispersion using galaxies with magnitudesr< 19.5. Some regions are dynamically complicated in ways that interfere with finding a simple relationship between dispersionσand linear mass densityμ. However, by examining individual overlapping segments along the filaments, we find a relationship that allows us to successfully predict $\log \mu$from $\log \sigma$with a scatter of about ±0.20 dex, for ∼70% of the regions along filaments. This relationship is robust to changes in the distance to the filament if the physical segment length and the absolute magnitude for galaxy selection are held constant. The relationship between redshift dispersion and mass is similar to that obtained for a simple analytical model where filaments are dynamically relaxed, and we examine the possibility that the galaxies are indeed relaxed within the gravitational potential of the filament. We find that this is not the case; galaxy dynamics are strongly affected by infall to the filament and by orbits within groups and clusters.