Cosmic velocity and tidal fields are important for the understanding of the cosmic web and the environments of galaxies, and can also be used to constrain cosmology. In this paper, we reconstruct these two fields in the Sloan Digital Sky Survey (SDSS) volume from dark matter haloes represented by galaxy groups. Detailed mock catalogues are used to test the reliability of our method against uncertainties arising from redshift distortions, survey boundaries and false identifications of groups by our group finder. We find that both the velocity and tidal fields, smoothed on a scale of ∼2 h−1 Mpc, can be reliably reconstructed in the inner region (∼66 per cent) of the survey volume. The reconstructed tidal field is used to split the cosmic web into four categories: clusters, filaments, sheets and voids, depending on the sign of the eigenvalues of local tidal tensor. The reconstructed velocity field nicely shows how the flows are diverging from the centres of voids, and converging on to clusters, while sheets and filaments have flows that are convergent along one and two directions, respectively. We use the reconstructed velocity field and the Zel’dovich approximation to predict the mass density field in the SDSS volume as function of redshift, and find that the mass distribution closely follows the galaxy distribution even on small scales. We find a large-scale bulk flow of about 117 km s−1 in a very large volume, equivalent to a sphere with a radius of ∼170 h−1 Mpc, which seems to be produced by the massive structures associated with the SDSS Great Wall. Finally, we discuss potential applications of our reconstruction to study the environmental effects of galaxy formation, to generate initial conditions for simulations of the local Universe, and to constrain cosmological models. The velocity, tidal and density fields in the SDSS volume, specified on a Cartesian grid with a spatial resolution of ∼700 h−1 kpc, are available from the authors upon request.