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Abstract The network of filaments with embedded clusters surrounding voids, which has been seen in maps derived from redshift surveys and reproduced in simulations, has been referred to as the cosmic web. A complementary description is provided by considering the shear in the velocity field of galaxies. The eigenvalues of the shear provide information regarding whether or not a region is collapsing in three dimensions, which is the condition for a knot, expanding in three dimensions, which is the condition for a void, or in the intermediate condition of a filament or sheet. The structures that are quantitatively defined by the eigenvalues can be approximated by iso-contours that provide a visual representation of the cosmic velocity (V) web. The current application is based on radial peculiar velocities from the Cosmicflows-2 collection of distances. The three-dimensional velocity field is constructed using the Wiener filter methodology in the linear approximation. Eigenvalues of the velocity shear are calculated at each point on a grid. Here, knots and filaments are visualized across a local domain of diameter .